Integrated and optimized distributed generation and interconnect system controller

ABSTRACT

Systems and methods for designing and controlling distributed generation resources are disclosed. Monolithic or distributed controllers control the power requests sent to each distributed generation resource to achieve optimal efficiency using rule-based and/or fuzzy logic-based control techniques. High-impedance fault (HIF) detection circuitry allows power export to the utility grid in normal operating circumstances, and when an islanding condition is detected, ceases that export within two seconds and prevents further export until the condition is cleared.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of PCT/US07/73900, having an international filing date of Jul. 19, 2007, which claims priority to U.S. Provisional Patent Application Ser. No. 60/807,786, filed Jul. 19, 2006, now expired.

TECHNICAL FIELD

The present invention relates to distributed power generation systems. More specifically, the present invention relates to systems that control or include a combination of distributed generation resources, one or more loads, and utility grids.

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1 is a block diagram of the functional components of a DG system controller described herein.

FIG. 2 is a block diagram of the hardware components of a DG system controller described herein.

FIG. 3 is a block diagram of a power management system according to the present disclosure.

FIG. 4 is a graph of system efficiency versus load power for optimal, rule-based, and load-following power distribution in a system having two 75 kw units.

FIG. 5 is a graph of load power output in a system having two 75 kw units.

FIG. 6 is a graph of system efficiency versus requested load power for optimal, equal-split and load-following power distribution strategies in a system having two 75 kw units.

FIG. 7 is a graph of unit load power versus total requested load power for a system of three 75 kw units.

FIG. 8 is a graph of system efficiency versus requested load power for optimal, equal-split and load-following power distribution strategies in a system having one 75 kw unit and one 150 kw unit.

FIG. 9 is a graph of unit load power versus total requested load power for a system of one 75 kw unit and one 150 kw unit.

FIG. 10 is a graph of total system efficiency versus total requested load power for a system of two 75 kw units and one 150 kw unit.

FIG. 11 is a graph of unit load power versus total requested load power for a system of two 75 kw units and one 150 kw unit.

FIG. 12 is a graph of total system efficiency versus total requested load power for a system of two 75 kw units and one 150 kw unit.

FIG. 13 is a graph of unit load power versus total requested load power for a system of one 75 kw unit and two 150 kw units.

FIG. 14 is a block diagram of a fuzzy controller for use in connection with any DG system.

FIG. 15 is a Matlab/Simulink model of a rule-based power distribution implementation for two 75 kw units.

FIGS. 16 (A) and (B) are Matlab/Simulink models of the “IF Action Subsystem” and “ELSE Action Subsystem,” respectively, for use in the model of FIG. 15, respectively.

FIG. 17 is a Matlab/Simulink model of a rule-based power distribution implementation for three 75 kw units.

FIGS. 18 (A), (B) and (C) are Matlab/Simulink models of subsystems for use in the “IF Action Subsystem,” “ELSEIF Action Subsystem,” and “ELSE Action Subsystem” of FIG. 17, respectively.

FIG. 19 is a Matlab/Simulink model of a rule-based and fuzzy rule-based power distribution implementation for a system having one 75 kw unit and one 150 kw unit.

FIGS. 20 (A), (B) and (C) are Matlab/Simulink models of subsystems for use in the “IF Action Subsystem,” “ELSEIF Action Subsystem,” and “ELSE Action Subsystem” of FIG. 19, respectively.

FIG. 21 is a fuzzy logic controller FIS structure for an “ELSE subsystem” in a system having two different distributed generator units.

FIG. 22 is a graph of fuzzy set membership functions for an “ELSE subsystem” in a system having two different distributed generator units.

FIG. 23 is a Matlab/Simulink model of a hybrid fuzzy rule-based power distribution implementation for controlling a system having two 75 kw units and one 150 kw unit.

FIGS. 24 (a) and (b) are Matlab/Simulink models of the “2ELSEIF Action Subsystem” and “ELSE Action Subsystem” for use in the model of FIG. 23.

FIG. 25 is a fuzzy logic controller FIS structure for an “ELSE subsystem” in a system having two different distributed generator units as illustrated in FIG. 23.

FIG. 26 is a graph of fuzzy set membership functions for an “ELSE subsystem” in a system having two different distributed generator units as illustrated in FIG. 23.

FIG. 27 is a Matlab/Simulink model of a hybrid fuzzy rule-based power distribution implementation for controlling a system with one 75 kw units and two 150 kw unit.

FIGS. 28 (A) and (B) are Matlab/Simulink models of the “2ELSEIF Action Subsystem” and “ELSE Action Subsystem” blocks for use in the model of FIG. 27.

FIG. 29 is a fuzzy logic controller FIS structure for an “ELSE subsystem” in a system having two different distributed generator units as illustrated in FIG. 27.

FIG. 30 is a graph of fuzzy set membership functions for an “ELSE subsystem” of two different distributed generator units as illustrated in FIG. 27.

FIG. 31 is a graph of a rule-based controller implementation for managing power distribution from two 75 kw units.

FIG. 32 is a graph of system efficiency of a rule-based implementation according to FIG. 31.

FIG. 33 is a graph of system efficiency for rule-based implementation and optimal power distributions in a system having two 75 kw units.

FIG. 34 is a graph of power output distribution in a rule-based controller implementation in a system having three 75 kw units.

FIG. 35 is a graph of system efficiency of a rule-based controller implementation for use in a system having three 75 kw units.

FIG. 36 is a graph of system efficiency in a rule-based controller implementation and an optimal power distribution scenario in a system with three 75 kw units.

FIG. 37 is a graph of unit power output in a hybrid fuzzy rule-based controller implementation in a system having one 75 kw unit and one 150 kw unit.

FIG. 38 is a graph of system efficiency for a hybrid fuzzy rule-based controller implementation in a system having one 75 kw unit and one 150 kw unit.

FIG. 39 is a graph of system efficiency under a hybrid fuzzy rule-based implementation and under an optimal power distribution scenario for a system having one 75 kw unit and one 150 kw unit.

FIG. 40 is a graph of unit power output under a hybrid fuzzy rule-based controller implementation a system having two 75 kw units and one 150 kw unit.

FIG. 41 is a graph of system efficiency in a hybrid fuzzy rule-based controller implementation in a system having two 75 kw units and one 150 kw unit.

FIG. 42 is a graph of system efficiency under a hybrid fuzzy rule-based controller implementation and the optimal power distribution for two 75 kw units and one 150 kw unit.

FIG. 43 is a graph of unit power output under a hybrid fuzzy rule-based controller implementation in a system having one 75 kw unit and two 150 kw units.

FIG. 44 is a graph of system efficiency under a hybrid fuzzy rule-based controller implementation in a system having one 75 kw unit and two 150 kw units.

FIG. 45 is a graph of system efficiency under a hybrid fuzzy rule-based controller implementation and optimal power distribution in a system having one 75 kw unit and two 150 kw units.

FIG. 46 is a block diagram of the functional components of a distributed generator system controller in one embodiment of the present invention.

FIG. 47 is a block diagram of the hardware components of a distributed generator system controller in one embodiment of the present invention.

FIG. 48 is a block diagram illustrating inputs and outputs to and from an engine in a distributed generator in one illustrated embodiment.

FIG. 49 is a block diagram of a quasi-static engine model.

FIG. 50 is a block diagram of an engine speed feedback control for use in various embodiments of the disclosed system.

FIG. 51 is a schematic diagram of a generator system.

FIG. 52 is a graph of internal voltage to excitor voltage under an open circuit condition (OCC).

FIGS. 53 (A) and (B) are a phasor and a schematic diagram of terminal voltage as used herein.

FIG. 54 is a block diagram of a generator system including certain control signals as used in various embodiments of the disclosed system.

FIG. 55 is a block diagram of an AVR and generator module for use some embodiments of the disclosed system.

FIG. 56 is a Simulink diagram of the AVR and generator module shown in FIG. 55.

FIG. 57 is a graph of power, voltage, and current in a simulated system during a load change event.

FIG. 58 is a graph of power, voltage, and current in a sine wave simulation during a load change event.

FIG. 59 is a graph of power, engine speed bias, and engine speed in a simulation of an engine speed feedback control (GIM) of one example system.

FIG. 60 is a block diagram of the engine speed feed-forward plus feedback control (GIM) in some embodiments of the disclosed system.

FIG. 61 is a graph of power, engine speed bias, and engine speed signals in a simulation of the control illustrated in FIG. 60.

FIGS. 62 (A) and (B) are a schematic diagram and phasor diagram, respectively, of power flow among a generator, loads, and tie-line in some embodiments of the disclosed system.

FIG. 63 is a block diagram of a feedback control system for maintaining a minimum power level from the grid.

FIG. 64 is a graph of simulation results from a controller in load-following mode (GPM).

FIG. 65 is a schematic diagram of a classical model of two generators with matching loads connected by a distribution line.

FIG. 66 is a graph of simulated frequency measurements from a DG unit before and after an islanding event.

FIG. 67 is a graph of the magnitude of the 1 Hz component of the DG signal shown in FIG. 66.

FIG. 68 is a graph of the trip and reset characteristics of an over-current relay for use in the disclosed system.

FIG. 69 is a schematic diagram of a transmission line in a fault condition.

FIG. 70 is a block diagram showing GENSETs and UICs as implemented in one embodiment of the disclosed system.

FIG. 71 is a flowchart illustrating error-handling logic in the controller in certain embodiments of the disclosed system.

FIG. 72 is a block diagram of a PC-based controller implementation of the current system.

FIG. 73 is a block diagram of functional components in the system shown in FIG. 72.

FIG. 74 is a circuit diagram of a PMU for use in the system shown in FIG. 72.

FIG. 75 is a block diagram of communication channels in a subsystem of the system shown in FIG. 72.

FIG. 76 is a graph of results obtained from a phasor calculation program for use in one embodiment of the disclosed system.

FIG. 77 is a schematic diagram of a phasor measurement unit (PMU) according to one embodiment of the disclosed system.

FIG. 78 is a block diagram showing communication between PMUs and the PC in the system illustrated in FIG. 72.

FIG. 79 is a one-line system diagram used to simulate high-impedance fault (HIF) detection techniques implemented in some embodiments of the disclosed system.

DESCRIPTION

For the purpose of promoting an understanding of the principles of the present invention, reference will now be made to the embodiment illustrated in the drawings and specific language will be used to describe the same. It will, nevertheless, be understood that no limitation of the scope of the invention is thereby intended; any alterations and further modifications of the described or illustrated embodiments, and any further applications of the principles of the invention as illustrated therein are contemplated as would normally occur to one skilled in the art to which the invention relates.

Generally, one embodiment of the present system implements par distribution strategies to improve overall system efficiency. Another embodiment provides an integrated and optimized distributed generation system control (DGSC) module that improves overall power generation performance and lowers the capital cost of distributed generation site installation in many implementations.

IEEE Standard 1547 (“the Standard”) provides a nationally recognized set of rules for connecting distributed power generation resources to a utility grid. This standard specifies requirements for voltage regulation, grounding, synchronization, inadvertent energizing, monitoring, protected relaying, power quality, islanding, and verification of compliance with itself. The subsequent IEEE Standard 1547.1 specifies test procedures for establishing and verifying compliance with the requirements of IEEE 1547. Some aspects of these standards will be discussed in further detail below.

Synchronous generators can regulate voltage and supply power to a local load even when they are not connected to the utility grid. DG units operating independently in grid-isolated mode (GIM) can provide primary or backup power when utility service is not available. However, DG facilities with synchronous machines also have the potential to supply voltage and power to a small piece of the utility grid that has been disconnected from the rest of the grid. This phenomenon is called islanding and it should generally be avoided for safety and other reasons. The IEEE 1547 standard requires that the DG detect islanded operation and cease to energize the utility grid within two seconds. The standard allows this requirement to be met using any of various island-detection schemes, as long as the selected method passes a test designed to create the most difficult circumstances for island-detection. That test requires an island to be detected when the DG and a matching load are simultaneously disconnected from the grid. Matching the load and DG output causes minimal frequency change when the grid is disconnected. Some systems currently on the market presently use the simplest technique to satisfy the islanding test, but this approach has an unfortunate drawback. The method simply disconnects the DG from the utility when the power imported from the utility falls below a preset threshold. The unfortunate drawback of this method is that it never allows export of power to the grid. As mentioned above, being able to export power to the grid is important for achieving maximum CHP efficiency. One aspect of the present system includes an island detection scheme that allows power export to the grid.

Proposed anti-islanding methods can be divided into two categories, namely, passive schemes and active schemes. Anti-islanding relays based on passive schemes include rate of change of frequency (ROCOF) relays and vector surge (VS) relays. Passive methods tend to perform poorly when the active power generated by the DG roughly balances the local load. Active methods overcome this limitation by introducing a small perturbation signal into the DG system. When the utility remains connected, the small disturbance caused by the intentional perturbation is not sufficient to trip island-detection relays. However, if the connection to the grid is lost, the response to the perturbation becomes large enough to activate island-detection relays. The challenge of active methods is to keep the perturbation small enough to avoid stability and power quality problems but large enough to cause a rapidly detectable response once the grid is lost.

Some forms of the present system include an optimized controller that allows a system to satisfy the requirements if IEEE 1547 and still export power to the grid with a system that could be used in many different jurisdictions. Built-in regulation features and anti-islanding capability in some embodiments provide operational benefits including more efficient power generation. In addition, the system's ability to export unneeded power to the grid allows distributed generation capacity to be sized by thermal load requirements for more efficient operation. Still further, some embodiments of the system provides significant capital- and installation-cost savings. Some embodiments incorporate relay components into a turn-key controller that eliminates the need for a trained technician to travel to an installation site to program the controller. Factory testing of some embodiments eliminates costly on-site installation delays. Still further, the supervisory control scheme in several embodiments allows users to add distributed power generation modules over time without undue additional engineering effort.

The present disclosure is presented in two parts. The first is directed primarily to a control system that optimizes distributed generation of power by homogeneous and heterogeneous collections of generators. The second part discusses additional aspects of the distributed power generation system.

Part 1—Optimized Controller

The power management system plays a key role in improving the overall system efficiency for multiple distributed generation units. The system performance, such as fuel economy, depends in part on the power management system strategy. The two conventional rule-based power distribution methods used in one existing design are quite simple, and only have been applied to two units. One method is to split the power equally between two identical units, and the other method is that the master unit always run full load, and the slave unit takes the rest of the load. These two conventional methods are not the optimal power distribution strategy.

This Part describes optimal power distribution strategies to improve overall system efficiency. A sequential quadratic programming method will be applied to find the optimal power distribution among multiple units. The optimal power management system is an important control function of the system control. This Part not only describes the optimal strategies for two identical units, but also describes strategies for three identical units, two different units, and three different units. Simulation results show that the disclosed optimal power management system can improve the system efficiency over the certain rule-based power management system.

A challenge to the full deployment of distributed energy is the fact that the electric power grid system is under the authority of hundreds of utilities and regulatory commissions. Developing a secure distributed generation (DG) system of energy production is hindered by the wide variety of technologies to produce power and the various grid suppliers' requirements for power acceptance.

A purpose of the present disclosure is to describe an integrated and optimized DG system controller module that improves the overall power generation performance attributes, and lowers the capital cost of a distributed generation site installation. The proposed system is intended to leverage the newly released IEEE 1547 Standard for Interconnecting Distributed Resources with Electric Power Systems that has defined a nationally recognized standard for grid interconnect for DG resources.

The overall DG system controller functional units include a supervisory controller, a DG unit controller, utility interface controller (UIC), and a DG unit protection functions and multiple unit configurations. Based on the operation of the system, the control system can be characterized as a hierarchical control structure with three distinct levels: supervision, coordination, and execution. The supervisory controller, which includes the UIC, is in the supervision level controller. The DG unit controller is in the coordination level. The execution level includes engine, engine control module (ECM), generator, and automatic voltage regulator (AVR) components.

This Part describes optimal power management strategies for multiple DG units, which is a significant function of the system controller. One objective of the optimal power management system (PMS) is to find an optimal way to distribute load power among multiple units to improve system efficiency. In this Part, the optimal PMS of the DG system is described. The optimal rule-based approach, a hybrid fuzzy rule-based PMS will distribute power among multiple DG units, which can optimize the entire system efficiently.

Certain existing power distribution systems are only used for power distribution between two units, and power distribution methods are quite simple. Two conventional methods in the existing art to distribute power between two DG units in industry involve either splitting the power equally between these two identical units, or a load-following method (the master unit always runs full load, and the slave unit takes the rest of the load). These two conventional methods are not optimal power distribution strategies. In this Part, the optimal power distribution strategies are shown to improve the overall system efficiency. The sequential quadratic programming (SQP) method is applied to find the optimal power distribution between multiple units. The theoretical derivation is presented for the problem. Before introducing the optimization, the overall control structure of the DG system is presented. The optimization and implementation of the optimal PMS will be one layer of the system control. This Part develops the optimal strategies for two identical units, for three identical units, for two different units and for three different units.

Optimal rule-based systems and hybrid fuzzy rule-based systems are designed in this disclosure for different configurations. In this Part, the fuzzy logic rules are tuned according to the optimal solution data. The controller for the DG unit is implemented and tested in hardware and software.

1.2. Main Subjects of this Part

-   -   Find optimal power distribution among multiple units by using         SQP.     -   Compare optimal PMS with existing power distribution methods.     -   Show design of rule-based PMS for identical units.     -   Show design of Hybrid fuzzy rule-based PMS for different units.

1.3. Organization of the Part

In this Part, the preceding issues are organized as follows: Chapter 2 discusses distributed generation systems, system controller architecture, and simulation model development for the DG unit. Chapter 3 describes optimal power management and control strategies, finds optimal load distribution solutions among multiple DG units, and compares optimal strategies with the two conventional methods. Chapter 4 describes two implementation methods, which are rule-based optimal power distribution and hybrid fuzzy rule-based optimal power distribution. In Chapter 4, the implementation results also are analyzed. Finally, Chapter 5 summarizes the teachings of this disclosure.

2. DG System and System Controller Architecture

2.1. Principles of DG

The DG unit in many embodiments can be used as a backup power supply for industry, and it also can sell electricity to the power grid. In one embodiment, a DG unit is an internal combustion engine generating system with a synchronous generator. In other embodiments DG engines are gasoline engines, diesel engines, and natural gas engines. The DG unit discussed in this Part is a natural gas fueled engine driving a synchronous generator that produces 60 Hz three-phase electrical power at 277/480 VAC under ISO standard conditions. Two types of DG units will be discussed in this Part. Their rated output powers are 75 kw and 150 kw, respectively.

Other embodiments will use other energy sources and have other output ratings or other characteristics. In these embodiments, the DG unit can work in grid isolated mode (GIM) or grid parallel mode (GPM) mode. DG units are connected to the local utility power grid in GPM or to the local site distribution bus in GIM.

2.2. DG System Control Architecture

The overall structure of the DG multiple units system is a hierarchical system, which is illustrated in FIG. 1. The DG system controller coordinates the control of one or more DG units as shown in FIG. 1. The system controller is capable of controlling up to 8 parallel DG units that are connected to the local utility grid in GPM or to the local site distribution bus in GIM. In this Part, controlling 2-3 parallel units will be discussed. It can be seen from FIG. 1 that the DG subsystem modules communicate with a supervisory controller. The supervisory controller performs the UIC functions.

There are two types of controllers in this embodiment: the DG unit controllers and the supervisory controller. A DG unit controller controls a single DG unit, while the supervisory controller coordinates the operation of multiple units in a single location. The functions of the supervisory controller are:

-   -   Grid synchronization and protection of the DG unit     -   Human/automatic switch between GPM/GIM     -   Control of human machine interface (HMI)     -   Communication among multiple units and external DG gateway

This Part will discuss the supervisory controller. There are two major functions of the supervisory controller that will be mentioned. The first function is controlling the GIM/GPM mode switch. The second is distributing load power among multiple units to maximize the system efficiencies by using a built-in power management system. The power management system will be the focus of this Part and will be discussed in the remaining chapters. Table 2.1 shows the supervisory control functions for the GIM/GPM mode switch. The switch is a logic control.

The DG system can run in GIM or GPM. Each DG unit will be running at either speed control mode or torque control mode according to the situation. The supervisory controller will determine the control mode of each DG unit. Table 2.1 shows the basic rules.

TABLE 2.1 Supervisory control functions for GIM/GPM mode switch (logic control) Configuration GIM GPM Single DG unit Voltage-regulating speed control Voltage-following torque control Multiple Determine master unit. All units use Voltage- DG units One master unit uses Voltage- following regulating speed control, torque control. other units use Voltage- following torque control.

FIG. 2 shows hardware-oriented block diagram for this embodiment of a DG system. It can be seen from FIG. 2 that each system controller includes a supervisory controller. Then supervisory controller communicates with other units to determine the master unit and slave units, and then determines the load power percentage for each unit when there are multiple units. A Phasor Measurement Unit (PMU) was used to measure the phasor of load power and then control the circuit break.

Additionally, the system controller includes a GIM/GPM switch control, load-following mode control, and UIC and DG unit controller. The GIM/GPM control is a digital logical control used to switch modes between GIM and GPM. The DG supervisory controller and UIC are preferably housed in a single enclosure (being in some cases a unitary housing, and in others a plurality of housings connected detachably or non-detachably by conduit or other substantially sealed passage), though in some embodiments they are in unconnected cases.

A PMS was developed for the DG system controller. The PMS is at the supervisory control level. An objective of the PMS is to manage the power distribution and coordinate among multiple units to improve the system efficiency. The execution level includes the DG unit controller, the engine, and the generator used to perform the specific tasks according to the desired commands generated by the PMS. The PMS accepts the signals from the supervisory controller and determines the splitting power demand to each DG unit controller using predefined strategies. The PMS also converts the load power demand to torque commands, which are sent to the DG unit controller as a load disturbance. There are several ways to distribute power among multiple units. Equal-split load power and load-following methods are used in some systems because they are easy to implement. However, these two methods are not the optimal power distribution methods. In this Part, an optimal power distribution system is described to optimize the entire system efficiency when multiple DG units are used. Chapter 3 characterizes the system efficiency problem and solves it mathematically using the Matlab optimization toolbox. In Chapter 4, the implementations of the optimal power management strategies are shown in Matlab/Simulink. The implementations are rule-based and hybrid fuzzy/rule-based power distribution.

3. Optimal Load Power Distribution Among Multiple Units

3.1. Power Management System Reviews

Power management is one of the functions in the supervisory controller. The system performance, such as the fuel economy, depends on the power management strategy.

The PMS is at the supervisory control level. The primary objective of the PMS is to manage the power distribution and coordinate among multiple units to improve system efficiency.

3.1.1. Inputs and Outputs

The inputs and outputs of the PMS module in this embodiment are illustrated in FIG. 3. Its input signal reflects the total required load power. Its outputs are the required load power values for each unit. For example, if there are three units, then the PMS has three output signals. The PMS accepts the signals from the supervisory controller and determines the assignment of power generation to each DG unit controller using predefined strategies. The PMS then converts the load power demand to torque commands, which will be sent to the DG engine controller.

3.1.2. Optimal PMS

Two very simple rule-based methods are used for power distribution among multiple DG units in some existing systems. These two methods were developed on the basis of simple analysis of component efficiencies and these two modes can be switched manually. One method is load-following by a single unit while all the other units are supplying no load or full load. The other method is to split power equally between multiple units.

These rule-based PMSs, although easy to implement, yield far from the optimal system efficiency. Moreover, they cannot determine whether the system efficiency is optimal or not.

There should in fact be an optimal power distribution among multiple DG units that maximizes the system efficiency. An optimal PMS can optimize the system-wide fuel efficiency for multiple units.

There are several approaches to designing an optimal PMS. Math-optimal PMS (such as SQP or dynamic programming (DP)) can achieve the exact optimal efficiency. However, this is often too time-consuming for online calculation. Rule-based PMS is easy to use, but it is practically limited to simple optimization rules; otherwise it will be difficult to obtain the rules, and will be time consuming to apply. Fuzzy PMS is not as precise as math-model based PMS (SQP or DP); however, it is convenient and fast for online implementation. If a look-up table is used, it can be more precise than a fuzzy system if there is sufficient optimal data in the look up table. A comparison among these five PMS design approaches is given in Table 3.1.

TABLE 3.1 Comparison of five PMS design approaches Method Advantages Disadvantages Rule-based Simple, easy to implement Intuitive, difficult to obtain exact rules SQP Well developed nonlinear Static optimization optimization method DP Global optimization Time consuming, the future load profile is needed Fuzzy rule- Practical, robust, easy to Difficult to obtain expert based implement online data to design fuzzy rule Look up Practical, easy to implement Not robust against table online environmental variations

3.2. Optimal PMS Design Procedure for DG System

The design procedure preferably begins with formulating the problem, defining a cost function, and then selecting a reliable and state-of-the-art optimization algorithm. The algorithm is preferably applied to minimize the cost function and optimize power distribution among multiple units. Finally, the feasible control rules, summarized from the statistical analysis of the optimal solution, are employed to develop a PMS for online power distribution implementation. The performance of the power management strategy is validated in the DG unit model, described herein. Finding the optimal power distribution will be described in this chapter.

3.3. Introduction to SQP

A cost function was developed that included a set of constraints. The cost function of system efficiency includes distributed load power for each unit, and an efficiency map of each unit. The power distribution was formulated as a constrained nonlinear optimization problem. In the meantime, the system efficiency should be maximized and a set of constraints should be satisfied.

SQP techniques are applied to solve the optimization problem. The optimizer can make well-informed decisions regarding directions of search and step length. The SQP subroutine in the Matlab optimization toolbox performs these steps:

-   -   1. Initialize;     -   2. Calculate the gradient of the cost function given the         constraints;     -   3. Define a positive definite Hessian matrix using the BFGS         formula based on the cost function and constraints;     -   4. Solve the quadratic programming (QP) problem using a modified         simplex method;     -   5. Use linear search and merit function method to determine the         new search direction and step size;     -   6. Check whether the termination criterion is satisfied; if not,         then go to step 2.

It can be seen that in this embodiment, at each iteration of the SQP method, a QP sub-problem is solved, and an estimate of the Hessian of the Lagrangian is updated at each iteration using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) Formula. Therefore, the SQP method converts the original optimization problem to a QP problem using the quadratic approximation of the objective function and the constraints. The SQP method closely mimics Newton's method for constrained optimization just as is done for unconstrained optimization. At each major iteration, an approximation is made of the Hessian of the Lagrangian function using a quasi-Newton updating method. This is then used to generate a QP sub-problem whose solution is used to form a search direction for a line search procedure.

3.4. How to Optimize the Problem in Matlab

In the Matlab optimization toolbox, the functions fmincon, fminimax, fgoalattain, and fseminf each use SQP. Among them, fmincon attempts to find a minimum of a constrained nonlinear multivariable function starting at an initial estimate. This is generally referred to as constrained nonlinear optimization or nonlinear programming.

3.5. Initial Value xo

The fmincon function does work properly, but the function fmincon will usually return a local minimizer in the vicinity of the starting point that the user supplies. If the model has more than one local minimizer, then different answers may be obtained for different starting points because the solver may converge to different solutions depending on the starting point. The user, using knowledge about the problem, provides the initial start point. Therefore, one should choose the initial vector xo to be in the feasible set.

If the problem has more than one local minimizer, a common approach is to sample the problem domain and optimize from different initial guesses. Therefore, all the local minimizers should be found and then the global minimum should be searched from those local minimizers.

A second option to increase the chances of finding the global minimizer for a nonlinear function is to run a genetic algorithm (GA), like the GA solver in the Genetic Algorithm and Direct Search Toolbox. However, this algorithm does not admit nonlinear constraints. A third option is to run PATTERNSEARCH solver, which admits nonlinear constraints.

A fourth option is to obtain all the local optimizers of different starting points xo by sampling the domain of the variables. Because the optimal minimizer is not only one point, but rather, a sequence of data points, the problem was divided into several regions. In each region, the problem domain was sampled from different initial guess xo. The global minimizer was then obtained.

3.6. Problem Formulations and Solutions

The optimization problem can be formulated as follows.

To maximize system efficiency f=f (x_(i)); is the same as minimizing F=1/f(x_(i));

Subject to Constraints: x ₁ +x ₂ + . . . +x=P _(out); 0≦x ₁≦c₁; 0≦x ₂≦c₂; 0≦x ₃≦c₃; . . . 0≦x _(i)≦c_(i)

In the experiments described in this Part, two types of DG units were used. One type is a 75 kw unit; the other is a 150 kw unit. Five different configurations are discussed:

-   -   Two identical 75 kw units.     -   Three identical 75 kw units.     -   Two different units with one 75 kw and one 150 kw.     -   Three different units with two 75 kw and one 150 kw unit.     -   Three different units with one 75 kw unit and two 150 kw units.

The system efficiency optimization for each of these five scenarios will be analyzed herein. Each configuration will be formulated with a certain cost function. With each of these cost functions, the SQP method was used to obtain the optimized solutions by using the Matlab optimization toolbox. Two identical 75 kw units will be evaluated first.

3.6.1. Two Identical 75 kw Units

3.6.1.1. Problem Formulation

The total system efficiency is derived as follows:

$\begin{matrix} {{{System}\mspace{14mu}{efficiency}} = \frac{{Total}\mspace{14mu}{output}\mspace{14mu}{power}}{{Total}\mspace{14mu}{input}\mspace{14mu}{power}}} \\ {= \frac{{Total}\mspace{14mu}{load}\mspace{14mu}{power}\mspace{14mu}{request}}{\left( {{{unit}\mspace{14mu} 1\mspace{14mu}{input}\mspace{14mu}{power}} + {{unit}\mspace{14mu} 2\mspace{14mu}{input}\mspace{14mu}{power}}} \right)}} \\ {= \frac{{Total}\mspace{14mu}{load}\mspace{14mu}{power}\mspace{14mu}{request}}{\left( {\frac{{unit}\mspace{14mu} 1\mspace{14mu}{output}\mspace{14mu}{power}}{efficiency} + \frac{{unit}\mspace{14mu} 2\mspace{14mu}{output}\mspace{14mu}{power}}{efficiency}} \right)}} \\ {{= \frac{P_{total}}{\left( {{x_{1}/{\eta\left( x_{1} \right)}} + {x_{2}/{\eta\left( x_{2} \right)}}} \right)}};} \end{matrix}$

Where, P_(total) is the total load power request, x₁ and x₂ are the distributed load power for unit 1 and unit 2 respectively; η is the efficiency map, which is a curve representing efficiency vs. output power. Original efficiency data was obtained from a company, and the efficiency function q was obtained by curve fitting. For a given P_(total), the above efficiency maximization problem is the same as minimizing the following cost function:

Minimize: F=x ₁/η(x ₁)+x ₂/η(x ₂); x ₁ +x ₂ =P _(total);

subject to: 0≦x ₁≦75 kw; 0≦x ₂≦75 kw.

It is a nonlinear optimization problem with linear constraints. The SQP was used to solve this problem in Matlab. The next subsection shows the optimal efficiency solution.

3.6.1.2. Optimal Solution Results for Two Identical 75 kw Units

The optimal solution results are depicted in FIG. 4. The X-axis represents the total load power request, and the Y-axis represents system electrical efficiency. There are three power distribution methods underlying this graph. The first method is the optimal power distribution, which is the continuous line. The second method is the equal split power method, which is represented by the “+” curve, and the third method is the load following method, which is represented by the “o” curve. Load following in this case means one unit runs as the master unit and always takes the load power. When the master unit alone is not enough for the total load power request, then the second unit takes the remaining load power. This continues when there are more than two units. From the graph, we can see that the system efficiency of optimal power distribution has higher performance than that of equal split method or load following method when power is distributed between two 75 kw units.

We also can see that when the total load power request is less than or equal to 75 kw, the optimal efficiency is almost the same as load following mode. When the total load power request is greater than 75 kw, the optimal efficiency is almost the same as the equal split mode. FIG. 5 shows how optimal PMS distributes power between these two 75 kw units.

There is a pattern in the optimal solution. When the total load power request is less than or equal to 75 kw, only unit 1 runs and unit 2 does not run. When the total load power request is greater than 75 kw, the power is split equally between unit 1 and unit 2.

3.6.2. Three Identical 75 kw Units

3.6.2.1. Problem Formulation

The total system efficiency is derived as follows: System efficiency=P _(total)/(x ₁/η(x ₁)+x ₂/η(x ₂)+x ₃/η(x ₃)); Where x₁, x₂, and x₃ are the power generation assignments for unit 1, unit 2, and unit 3, respectively. The above efficiency maximization problem for a given P_(tota1) is the same as minimizing the following cost function:

Minimize: F=x ₁/η(x ₁)+x ₂/η(x ₂)+x ₃/η(x ₃); x ₁ +x ₂ +x ₃ =P _(total); Subject to: 0≦x ₁≦75 kw; 0≦x ₂≦75 kw; 0≦x ₃≦75 kw; This is a nonlinear optimization problem with linear constraints. The SQP was used to solve it in Matlab.

3.6.2.2. Optimal Solution Result for Three Identical 75 kw Units

The optimal solution results are depicted in FIG. 6. From the graph, we can see that the system efficiency of optimal power distribution has higher performance than that of the equal split method or the load following method for this configuration.

We also can see that when the total load power request is less than or equal to 75 kw, the optimal efficiency is almost the same as the load following mode. When the total load power request is greater than 150 kw, the optimal efficiency is almost the same as the equal split mode. FIG. 7 shows how optimal PMS distributes power among these three 75 kw units.

There is a logical pattern in the optimal solution. When the total load power request is in the interval of [0 75] kw, only unit 1 runs. When the total load power request is in the interval of (75 150] kw, the power is split equally between unit 1 and unit 2, and unit 3 does not run. When the total load power request is in the interval (150 225] kw, the power is split equally among three units, as in equal split mode. Two different units will be evaluated now. When identical units are not used, there is no obvious pattern in some regions.

3.6.3. Two Different Units with One 75 kw Unit and One 150 kw Unit

3.6.3.1. Problem Formulation

The total system efficiency is derived as follows: System efficiency=P _(total) /x/η ₁(x ₁)+x ₂/η₂(x ₂)); Where, x_(i) is for 75 kw unit, x₂ is for 150 kw unit and η₂ is the efficiency map for 150 kw unit. In this configuration, η₁ and η₂ are different functions.

The above efficiency maximization problem for a given P_(total) is the same as minimizing the following cost function:

Minimize: F=x ₁/η₁(x ₁)+x ₂/η₂(x ₂); Subject to: x ₁ +x=P _(total); 0≦x ₁≦75 kw; 0≦x ₂≦150 kw. This is a nonlinear optimization problem with linear constraints. The SQP was used to solve the problem in Matlab.

3.6.3.2. Optimal Solution for Two Different Units with One 75 Kw Unit and One 150 Kw Unit

The optimal solution results for this configuration are depicted in FIG. 8. When there are different units, there is no equal split mode, and there are two different load following methods. One method uses the 75 kw unit as the master unit with a 150 kw unit following. The other method uses a 150 kw unit as the master unit with a 75 kw unit following. These two load following methods can result in different system efficiencies. From the graph, we can see that the system efficiency of optimal power distribution has higher performance than that of load following methods when power is distributed between two different units.

We also can see that when the total load power request is in the interval of [0 75] kw, the optimal efficiency is almost the same as the first load following mode (75 kw unit as master). When the total load power request is in the interval of (75 150] kw, the optimal efficiency is almost the same as the second load following mode (150 kw unit as master). When the total load power request is in the interval of (150 225] kw, the optimal efficiency is different from either load following mode. FIG. 9 shows how optimal PMS distributes power between these two different units.

There is a pattern in the optimal solution. When the total load power request is in the interval of [0 75] kw, only the 75 kw unit (unit 1) runs. When the total load power request is in the interval of (75 150] kw, only the 150 kw unit runs, and the 75 kw unit does not run. When the total load power request is in the interval of (150 225] kw, then the total load power request is distributed between the 75 kw unit and the 150 kw unit. There is no obvious pattern for P_(total)>150 kw. Because of that, a fuzzy logic controller for online implementation was used in this region.

3.6.4. Three Different Units with Two 75 kw Units and One 150 kw Unit

3.6.4.1. Problem Formulation

The total system efficiency is derived as follows: System efficiency=P _(total)/(x ₁/η₁(x ₁)+x ₂/η₁(x ₂)+x ₃/η₂(x ₃)); Where, x₁, x₂, and x₃ are for one 75 kw unit, the other 75 kw unit, and a 150 kw unit, respectively. The above efficiency maximization problem for a given P_(total) is the same as minimizing the following cost function:

Minimize F=(x ₁/η₁(x ₁)+x ₂/η₁(x ₂)+x ₃/η₂(x ₃); Subject to: x ₁ +x ₂ +x ₃ =P _(total); 0≦x ₁≦75 kw; 0≦x ₂≦75 kw; 0≦x ₃≦150 kw.

This is a nonlinear optimization problem with linear constraints. The SQP was used to solve it in Matlab.

The optimal solution results are depicted in FIG. 10. There are three different load following methods for this configuration. One method is S-S-B; “S” indicates the small unit, 75 kw, and “B” indicates the big unit, 150 kw. For S-S-B, 75 kw unit (unit 1) was the master, and the other 75 kw unit (unit 2) follows as the second unit with the 150 kw unit (unit 3) following as the last unit. The other two methods are S-B-S and B-S-S. These three different load following methods can result in different system efficiencies. From the graph, it can be seen that the system efficiency of optimal power distribution has higher performance than that of the three load following methods when load power is distributed among these three different units.

3.6.4.2. Optimal Solution Result

It also can be seen from FIG. 10 that when the total load power request is less than or equal to 75 kw, the optimal system efficiency is almost the same as the system efficiency of the S-S-B and S-B-S load following methods. When the total load power request is in the interval of (75 300] kw, the optimal system efficiency is better than the system efficiency of all load following modes. FIG. 11 shows how optimal PMS distributes power among these three different units.

There is a logical pattern in the optimal solution. When the total load power request is in the interval of [0 75] kw, only the 75 kw unit (unit 1) runs. When the total load power request is in the interval of (75 150] kw, two 75 kw units (unit 1 and unit 2) split the total load power equally and the 150 kw unit (unit 3) does not run. When the total load power request is in the interval of (150 225] kw, one 75 kw unit (unit 1) does not run. The load power is distributed between the other 75 kw unit (unit 2) and the 150 kw unit (unit 3). There is no obvious pattern in this case. Because of that, a fuzzy logic controller for online implementation was used in this region. When the total load power request is in the interval of (225 300] kw, the load power is distributed between two 75 kw units and one 150 kw units. There is no obvious pattern in this case except that the two 75 kw units run at the same load power. Because of that, a fuzzy logic controller for online implementation was used in this region to distribute power between two 75 kw units and one 150 kw unit, and a mathematical rule is used at the same time to allow the two 75 kw units to provide identical output.

3.6.5. Three Different Units with One 75 Kw Unit and Two 150 Kw Units

3.6.5.1. Problem Formulation

The total system efficiency for this configuration is derived as follows: System efficiency=P _(total)/(x ₁/η₁(x ₁)+x ₂/η₁(x ₂)+x ₃/η₂(x ₃)); where x_(i) is for the 75 kw unit, both x₂ and x₃ are for the 150 kw units. For a given P_(total), the above efficiency maximization problem is the same as minimizing the following cost function:

Minimize: F=(x ₁/η₁(x ₁)+x ₂/η₂(x ₂)+x ₃/η₂(x ₃)); x ₁ +x ₂ +x ₃ =P _(total); Subject to: 0≦x ₁≦75 kw; 0≦x ₂≦150 kw; 0≦x ₃≦150 kw.

This is a nonlinear optimization problem with linear constraints. The SQP was used to solve the problem in Matlab.

3.6.5.2. Optimal Solution Results

The optimal solution results for this configuration are depicted in FIG. 12. There are three different load following methods for this configuration. For the S-B-B method, 75 kw unit (unit 1) was master and the 150 kw unit (unit 2) follows as the second with 150 kw unit (unit 3) following as the last unit. The other two methods are B-B-S and B-S-B. These three different load following methods can result in different system efficiencies. From the graph, it can be seen that the system efficiency of optimal power distribution has higher performance than that of three load following methods when load power is distributed among these three different units.

It also can be seen that when the total load power request is less than or equal to 75 kw, the optimal system efficiency is almost the same as the system efficiency of the SB-B load following method. When the total load power request is in the interval of (75 150) kw, the optimal system efficiency is the same as the system efficiency of B-S-B and B-B-S load following methods. When the total load power request is in the interval of (150 375] kw, the optimal system efficiency is better than that of all load following methods. FIG. 13 shows how optimal PMS distributes power among these three different units.

There is also a pattern in the optimal solution. When the total load power request is in the interval of [0 75] kw, only the 75 kw unit (unit 1) runs. When the total load power request is in the interval of (75 150] kw, only one of the 150 kw units (unit 3) runs and the other units do not run. When the total load power request is in the interval of (150 225] kw, one of the 150 kw units (unit 2) does not run and the load power is distributed between the 75 kw unit (unit 1) and another 150 kw unit (unit 3). There is no obvious pattern in this case. Because of that, the fuzzy logic controller illustrated in FIG. 14 was used in this region for online implementation. When the total load power request is in the interval of (225 300] kw, the 75 kw unit (unit 1) does not run, and the two 150 kw units (unit 2 and unit 3) equally split the total load power. When the total load power request is in the interval of (300 375] kw, the load power is distributed between one 75 kw unit and two 150 kw units, and there is no obvious pattern in this case except that the two 150 kw units run at the same load power. Because of that, a fuzzy logic controller for online implementation was used in this region to distribute power between one 75 kw unit and two 150 kw units, and a mathematical rule is used at the same time to allow the two 150 kw units to provide identical output.

3.7. Result Analysis and Comparison Between Different Configurations

3.7.1. Optimal Results Analysis

The simulation results of the above five configurations demonstrated that the proposed optimal PMS improved the system efficiency significantly compared to the current rule-based PMS. The next step is to implement the optimal PMS algorithm in real time.

3.7.2. Optimal PMS Implementation

The optimal PMS have several drawbacks:

-   -   1. The SQP algorithm has a complex structure; therefore, more         computing power would make the PMS online implementation more         feasible.     -   2. The optimal PMS design is not robust enough against the         environmental variations and external disturbances. The         efficiency map used in the optimization algorithm was based on a         specific temperature and altitude. Therefore, more efficiency         and robust PMS should be developed to distribute power among         multiple DG units.

In this Part, two methods are developed to implement optimal PMS. They are rule-based PMS and hybrid fuzzy rule-based (rule-based and fuzzy rule-based) PMS. The hybrid fuzzy rule-based PMS combined both crisp logic and fuzzy logic. Table 3.2 shows the control rules summarized from the statistical analysis of the optimal solution and the implementation methods for each configuration.

TABLE 3.2 Comparison of the optimal power distributions and their implementations for five different configurations Control rules summarized from the statistical analysis of the optimal solutions # Configuration P_(total) (kw) Unit 1 Unit 2 Unit 3 Implementation 1 Two identical 75 kw units [0 75] P_(total) 0 N/A Rule-based Unit 1-75 kw (75 150] /2 /2 N/A Unit 2-75 kw 2 Three identical 75 kw units [0 75] 0 0 Rule-based Unit 1-75 kw (75 150] /2 /2 0 Unit 2-75 kw (150 225] /3 /3 /3 Unit 3-75 kw 3 Two different units with [0 75] 0 N/A Hybrid fuzzy one 75 kw unit and one (75 150] 0 N/A rule-based 150 kw unit (150 225] x1 −x1 N/A Unit 1-75 kw Unit 2-150 kw 4 Three different units with [0 75] 0 0 Hybrid fuzzy two 75 kw units and one (75 150] /2 /2 0 rule-based 150 kw unit (150 225] 0 x2 −x2 Unit 1-75 kw (225 300] (−x3)/2 (−x3)/2 x3 Unit 2-75 kw Unit 3-150 kw 5 Three different units with [0 75] 0 0 Hybrid fuzzy one 75 kw unit and two (75 150] 0 0 rule-based 150 kw units (150 225] x1 −x1 0 Unit 1-75 kw (225 300] 0 /2 /2 Unit 2-150 kw (300 375] x1 (−x1)/2 (−x1)/2 Unit 3-150 kw

The rule-based PMS is constructed according to the math-optimal result; therefore, the resulting rule-based PMS is exactly the same as the math-optimal PMS. However, the rule-based PMS can only be used for simple optimization rules; otherwise it will be difficult to find exact rules and also will be very time consuming. The fuzzy PMS is not as precise as the rule-based PMS in this case; however, it approximates the math-optimal PMS and is convenient and fast for online implementation.

Based on the analysis of the optimal solution, the rule-based PMS was developed for identical units because there are some obvious patterns in their optimal solutions. And the hybrid fuzzy rule-based PMS were developed for different units because in some regions there are no obvious patterns for different units to split load power. Therefore, fuzzy logic was used in those regions for online implementation.

The implementation result will now be compared with optimal solution and those obtained from current PMS.

4. Implementation of Optimal Power Management System

4.1. Optimal Power Distribution Implementation

In Chapter 3, we used SQP to statically optimize the power distribution. The remaining problem is how to implement the PMS online. There are several methods to implement the optimal power distribution online. According to the optimal results, rule-based and fuzzy rule-based implementations are chosen in this Part. The rule-based system is simple and easy to implement. Generally speaking, it is intuitive, but difficult to obtain exact rules, and they apply well only to certain simple systems. Fuzzy rule-based systems, generally speaking, are practical, robust, and easy to implement online, but it is difficult to obtain expert data from which to design fuzzy rules. In this Part, fuzzy rules will be designed according to the optimal results that were obtained in Chapter 3.

4.1.1. Rule-based and Fuzzy Rule-based Implementation for Power Distribution

According to the optimization results, when identical units were used, certain patterns were apparent, and rules can be derived based on these results. The rule-based PMS configurations were thus designed for implementation. However, when different units are used, rule-based PMS is not so easily applied for different ranges of P total in certain regions. The optimal solutions can be divided into several regions. In some regions, the rule-based implementation was designed. In other regions, fuzzy logic was used to implement the power distribution. This hybrid power distribution was used for different units. The power distribution uses crisp logic and a fuzzy logic controller at the same time.

4.1.2. Introduction to Fuzzy Logic Controller

4.1.2.1. Fuzzy Logic System and Fuzzy Logic Controller Scheme

Fuzzy logic provides a general description and measurement of a system similar to human reasoning. In fuzzy logic, the truth of any statement is a matter of degree. A membership function is the curve that describes how true a given statement is for a given input value. Fuzzy logic does not use crisp values to describe a system; instead, human reasoning is used. For example, when describing the temperature, crisp values were not used. Instead, we use a “high,” “medium,” “low,” etc. fuzzy logic set. Different temperature values may belong to different fuzzy logic sets with a certain percentage membership. Fuzzy set membership occurs by degree over the range [0, 1]. For example, 100° F. might belong to a set of “high” temperatures, and its membership to the “high” fuzzy set is 0.7, and it may also belong to “medium” at the same time with a membership of 0.2.

Fuzzy logic systems can be used to make decisions or control systems by encoding human reasoning. Therefore a fuzzy logic system can easily be understood and built based on human understanding. Fuzzy logic comprises fuzzy sets, fuzzy set membership functions, fuzzy rules, and fuzzy inference. Fuzzy sets represent non-statistical uncertainty. A membership function is used to represent the fuzzy set membership. Triangle, trapezoid, Gaussian and sigmoid functions are commonly used as fuzzy set membership functions. Fuzzy rules approximate human reasoning, which used to make inferences in fuzzy logic. All the fuzzy rules in a fuzzy system are applied in parallel. The design procedure of the fuzzy logic controller in this Part works as follows.

-   -   Define input and output variables of a fuzzy logic controller.     -   Fuzzify the input and output variables. Define fuzzy sets and         fuzzy membership functions for each fuzzy variable.     -   Determine fuzzy rule set.     -   Defuzzify the fuzzy outputs to obtain the crisp values for each         output variable.

In this Part, the input signal to the fuzzy controller is the total load power request. The output signal is the load power to each single unit (75 kw or 150 kw unit). The diagram below shows the fuzzy logic controller scheme.

4.1.2.2. Design Fuzzy System Using Matlab/Fuzzy Logic Toolbox

In this work, the fuzzy logic toolbox in Matlab was used. Its graphic user interface (GUI) is easy to use to design fuzzy inference system (FIS) structure, fuzzy sets, fuzzy set membership functions, and fuzzy rule set. As long as the fuzzy system was properly designed, the fuzzy system can be represented as a FIS file in the fuzzy toolbox. When designing a fuzzy controller in Matlab/Simulink, the FIS file name must be provided in the fuzzy controller block parameter window, and when running the Simulink model, Simulink recalls the fuzzy system.

4.2. Rule-based and Hybrid Fuzzy Rule-based Implementation for Power Distribution in Matlab/Simulink for Five Different Scenarios

According to the optimal power distribution data, rule-based and fuzzy rule-based power distribution implementations are designed in a Matlab/Simulink environment. Simulation results also will be discussed in this section. In this section, the design of the rule-based and fuzzy rule-based power distribution Simulink models of each configuration will be discussed.

The models for every configuration are built according to the optimal power distribution results. The distributed load power signals were sent to each unit through multiport switches. Inside each unit there is a subsystem used to calculate input power and fuel consumption. Finally, the system electrical efficiency was calculated.

4.3. Two Identical 75 Kw Units

FIG. 15 shows the Simulink model of the rule-based power distribution implementation for two 75 kw units. Conventional logic is used in this model to distribute power between two 75 kw units (unit 1 and unit 2). FIG. 16 shows the IF and ELSE subsystems, which are built according to the rules obtained from the analysis of optimal power distribution data.

4.4. Three Identical 75 kw Units

FIG. 17 shows the Simulink model of the rule-based power distribution implementation for three 75 kw units. Crisp logic is used in this model to distribute power among three 75 kw units (unit 1, unit 2, and unit 3). FIG. 18 shows the IF, ELSEIF, and ELSE subsystems, which are built according to the rules obtained from the analysis of optimal power distribution data.

4.5. Two Different Units with One 75 Kw and One 150 Kw Unit

FIG. 19 shows the rule-based and fuzzy rule-based power distribution implementation for two different units. Both crisp logic and fuzzy logic are used in this model to distribute power between a 75 kw unit (unit 1) and a 150 kw unit (unit 2).

FIG. 20 shows the IF, ELSEIF, and ELSE subsystems, which are built according to the rules obtained from the analysis of optimal power distribution data. Both IF and ELSE subsystems are rule-based subsystems, but the ELSEIF subsystem is a fuzzy rule-based system. Inside this block is a fuzzy controller. The inputs of the fuzzy controller are the total load power request and heat request. The output signal is the load power for the 75 kw unit (unit 1). The load power for the 150 kw unit (unit 2) is equal to the total load power minus the load power of the 75 kw unit (unit 1). The fuzzy controller in this embodiment can only have an output for either the 75 kw unit (unit 1) or the 150 kw unit (unit 2), and cannot have outputs for each of these two units. If there are two outputs for the fuzzy controller, and when these two outputs are added together, the sum may not equal the total load power request. Because the controller used here applies fuzzy logic, the fuzzy controller may not provide the output values whose sum is exactly equal to the input total load power value.

4.5.1. Fuzzy Logic Controller Design for ELSE Subsystem

4.5.1.1. FIS Structure

When designing a fuzzy system, first define the inputs and outputs and their membership functions. Then construct fuzzy rules. The FIS structure represented by the fuzzy toolbox GUI is shown in FIG. 21.

There are one input, one output, and three rules in this FIS structure. Each input and output signal of the fuzzy system is a fuzzy variable, which has several fuzzy sets and their own fuzzy membership functions. The output signal in this case is the load power to the 75 kw unit.

4.5.1.2. Fuzzy Sets and Fuzzy Membership Functions

The fuzzy controllers in this Part have one input and one output as described in the fuzzy controller scheme. Each input and output has a different number of fuzzy sets; for example, for two different units, the fuzzy sets for input and output are:

-   -   Total load power request: Three fuzzy sets—H (high), M (medium),         L (low)     -   Unit 1 load power: Four fuzzy sets—H (high), M (medium), OK, L         (low)

In fuzzy logic, a value can partially belong to a fuzzy set with corresponding membership between 0 and 1. In this Part, trapezoid functions (include left-trapezoid function and right-trapezoid function) and triangle functions are selected as the membership functions. The entire rule set is applied in parallel, and fuzzification and defuzzification methods are used to obtain the output signal from the inputs. FIG. 22 shows the fuzzy sets and membership functions for the configuration of two different units.

4.5.1.3. Fuzzy Rule Set

The fuzzy rule set includes a set of fuzzy if-then rules, which define the fuzzy inference system from the input to output based on the optimal data.

The fuzzy control rule set shown in Table 4.1 is built based on human analysis of the optimal solution in Chapter 3.

TABLE 4.1 Fuzzy rule set 1. If (Total_Required_Power is L) then (Output_Power_1 is OK) (1) 2. If (Total_Required_Power is M) then (Output_Power_1 is M) (1) 3. If (Total_Required_Power is H) then (Output_Power_1 is H) (1)

4.5.1.4. Representation of Fuzzy System (FIS File)

In Matlab/fuzzy logic toolbox, the following method is used to represent a fuzzy system as shown in Table 4.2. This is also the FIS file.

TABLE 4.2 The representation of a fuzzy system in Matlab [System] Name=’PMS_5_2DIFF’ Type=’mamdani’ Version=2.0 NumInputs=1 NumOutputs=1 NumRules=3 AndMethod=’min’ OrMethod=’max’ ImpMethod=’min’ AggMethod=’max’ DefuzzMethod=’centroid’ [Input1] Name=’Total_Required_Power’ Range=[150 225] NumMFs=3 MF1=’L’:’trapmf’,[150.9 154.5 181.8 186] MF2=’M’:’trapmf’,[174.5 182.7 209.1 215.2] MF3=’H’:’trapmf’,[210 214.6 226.4 239 1] [Output] Name=’Output_Power_1’ Range=[0 75] NumMFs=4 MF1=’L’:’trapmf’,[0.5036 17.78 38.14 52.69] MF2=’OK’:’trapmf’,[44.55 50.5 60.45 66.82] MF3=’H’:’trapmf’,[71.49 72.67 77.49 80.22] MF4=’M’:’trapmf’,[61.94 66.12 72.12 75.12] [Rules] 1, 2 (1) : 1 2, 4 (1) : 1 3, 3 (1) : 1

The first section shows general information about the system, which includes number of inputs, outputs, and rules. The first section also includes fuzzification and defuzzification methods. As the above table shows, there are one input, one output, and three rules. The remaining sections show the information about each input and output fuzzy variable, which include the name, fuzzy sets and their membership functions, and fuzzy rules of each input and output variable. For the membership functions, information about the name, type, and range of each membership function is indicated. For the fuzzy rule set, the above FIS file lists three rules. Each line was encoded from a rule provided in Table 4.1. The first integer represents the input and the second integer represents the output. “1” means membership function 1, which is “L” (low), and “2” means membership function 2, which is “M” (medium) and so on. The number in parentheses is the weight of the rule. The last number is the rule connection. For example, the first line shows: “1, 2 (1): 1,” which line represents the first rule listed in Table 4.1. This rule is as follows:

-   -   If (Total_Required_Power is L) then (Output Power 1 is OK)         (weight 1)

4.6. Three Different Units with Two 75 Kw Units and One 150 Kw Unit

FIG. 23 shows the hybrid fuzzy rule-based power distribution implementation for three different units with two 75 kw units and one 150 kw unit. Both crisp logic and fuzzy logic are used in this model to distribute power among two 75 kw units (unit 1 and unit 2) and a 150 kw unit (unit 3).

FIG. 24 shows the IF, ELSELF, and ELSE subsystems, which are built according to the rules in Table 4.3. For the ELSEIF2 subsystem, the output signal of the fuzzy controller is the load power for the 75 kw unit (unit 1). The load power for the 150 kw unit (unit 3) is equal to the total load power request minus the load power of the 75 kw unit (unit 1). The other 75 kw unit (unit 2) does not run. For the ELSE subsystem, the output signal of the fuzzy controller is the load power for the 150 kw unit (unit 3). The two 75 kw units (unit 1 and unit 2) equally share the remaining load power.

The fuzzy logic controller in the ELSEIF2 subsystem in FIG. 24 is the same controller as used for two different units, but the fuzzy logic controller in the ELSE subsystem is different.

4.6.1. Fuzzy Logic Controller Design for the ELSE Subsystem

4.6.1.1. FIS Structure

There are one input, one output, and four rules in the FIS structure illustrated in FIG. 25. The output signal in this case is the load power to the 150 kw unit (unit 3). The output is different from that of the previous fuzzy controller.

4.6.1.2. Fuzzy Sets and Fuzzy Membership Functions

The fuzzy sets for input and output are as illustrated in FIG. 26:

-   -   Total load power request: four fuzzy sets—H (high), M (medium),         OK, L (low)     -   Unit 3 load power: four fuzzy sets—H (high), M (medium), OK, L         (low)

4.6.1.3. Fuzzy Rule Set

The fuzzy rules for this fuzzy logic controller are shown in Table 4.3.

TABLE 4.3 Fuzzy rule set 1. If (Total_Required_Power is L) then (unit_3 is L) (1) 2. If (Total_Required_Power is M) then (unit_3 is M) (1) 3. If (Total_Required_Power is H) then (unit_3 is H) (1) 4. If (Total_Required_Power is OK) then (unit_3 is OK) (1)

4.7. Three Different Units with One 75 kw Unit and Two 150 kw Units

FIG. 27 shows the hybrid fuzzy rule-based power distribution implementation for three different units with one 75 kw unit and two 150 kw units. Both crisp logic and fuzzy logic are used in this model to distribute power among a 75 kw unit (unit 1) and two 150 kw units (unit 2 and unit 3).

FIG. 28 shows the IF, ELSEIF, and ELSE subsystems, which are built according to the rule obtained from the analysis of optimal power distribution data. For the ELSEIF2 subsystem, the load power for the 150 kw unit (unit 2) is equal to the total load power minus the load power of the 75 kw unit (unit 1). The other 150 kw unit (unit 3) does not run. For the ELSE subsystem, both 150 kw units (unit 2 and unit 3) share the remaining load power request equally.

The fuzzy logic controller in the ELSEIF2 subsystem is the same controller as used for two different units, but the fuzzy logic controller in the ELSE subsystem is different from previous fuzzy controllers. The fuzzy sets, membership functions, and rule set are totally different.

4.7.1. Fuzzy Logic Controller Design for the ELSE Subsystem

4.7.1.1. FIS Structure

FIG. 29 shows the FIS structure of the fuzzy controller. There are one input, one output, and 5 rules in this FIS structure. Output signal in this case is the load power request to the 75 kw unit (unit 1).

4.7.1.2. Fuzzy Sets and Fuzzy Membership Functions

The fuzzy sets for inputs and outputs are as illustrated in FIG. 30:

-   -   Total load power request: five fuzzy sets—VH (very high), H         (high), M (medium), OK, L (low)     -   Unit 1 load power: five fuzzy sets—VH (very high), H (high), M         (medium), OK, L (low)

4.7.1.3. Fuzzy Rule Set

The fuzzy rules for this fuzzy logic controller are shown in Table 4.4.

TABLE 4.4 Fuzzy rule set 1. If (Total_Required_Power is L) then (unit_1 is L) (1) 2. If (Total_Required_Power is H) than (unit_1 is H) (1) 3. If (Total_Required_Power is M) than (unit_1 is M) (1) 4. If (Total_Required_Power is OK) than (unit_1 is OK) (1) 5. If (Total_Required_Power is VH) then (unit_1 is VH) (1)

4.8. Simulation Results of Rule-based and Hybrid Fuzzy Rule-based Implementations for Power Distribution with Five Different Configurations.

4.8.1. Two Identical 75 kw Units

For two identical 75 kw units, FIG. 31 shows the rule-based power distribution implementation design using Matlab/Simulink according to the optimal power distribution result FIG. 31 shows how the PMS splits power between two units.

The first row shows the total load power request, which increases with time as a ramp signal. The second row shows the load power distributed to a 75 kw unit (unit 1). The third row shows the load power distributed to the other 75 kw unit (unit 2). It can be seen that when the total load power request is less than 75 kw, only unit 1 runs and unit 2 does not run. When the total load power request is greater than 75 kw, unit 1 and unit 2 split the load power equally.

FIG. 32 shows the total electrical efficiency by using this rule-based power management system. The first row shows the total load power request, which increases with time as a ramp signal. The second row shows the total system electrical efficiency. It can be seen that when the total load power request reaches 75 kw, unit 1 ran full load, and the system electrical efficiency achieved its highest point. It is approximately 31%. When the total load power request is 150 kw, both units run full load, and the system electrical efficiency also achieve its highest point.

This system electrical efficiency is satisfactory if compared with the optimal efficiency. This can be seen from FIG. 33. The continuous line indicates the system total efficiency of rule-based implementation for two 75 kw units. The “o” curve indicates the system electrical efficiency of optimal power distribution. It can be seen that the system electrical efficiency of the rule-based implementation is almost exactly the same as that of the optimal power distribution. It is noted that the optimal efficiency is slightly lower than that obtained in the rule-based implementation at a few points due to numerical round off error.

4.8.2. Three Identical 75 kw Units

For three identical 75 kw units, FIG. 35 shows the rule-based performance in a static simulation.

FIG. 34 shows how the PMS splits power among three 75 kw units.

It can be seen that when the total load power request is less than 75 kw, only unit 1 runs, and neither unit 2 nor unit 3 run. When the total load power request is greater than 75 kw and less than 150 kw, unit 1 and unit 2 split the load power equally. When the total load power request is greater than 150 kw, three units split power equally.

FIG. 35 shows the total electrical efficiency by using this rule-based power management system. It can be seen that when the total load power request reaches 75 kw, unit 1 ran full load, and the total electrical efficiency achieve its highest point. It is approximately 31%. When the total load power request reaches 150 kw, both unit 1 and unit 2 ran full load, and the system electrical efficiency also achieve its highest point. When the total load power request reaches 225 kw, three units ran full load and the system electrical efficiency also achieve its highest point.

This system electrical efficiency is satisfactory if compared with the optimal efficiency. This can be seen from FIG. 36.

It can be seen that the system electrical efficiency of rule-based implementation is almost the same as that of the optimal power distribution. This is the power distribution for three 75 kw units. Power distribution for two different units with one 75 kw unit and one 150 kw unit will now be evaluated.

4.8.3. Two Different Units with One 75 kw Unit and One 150 kw Unit

For two different units, hybrid fuzzy node-based implementation was used for power distribution in Matlab/Simulink according to the optimal power distribution results. FIG. 37 shows how the PMS split power between two different units.

It can be seen from the graph that when the total load power request is less than 75 kw, only the 75 kw unit (unit 1) runs and the 150 kw unit (unit 2) does not run. When the total load power request is greater than 75 kw and less than 150 kw, only the 150 kw unit (unit 2) runs and the 75 kw unit (unit 1) does not run. When the total load power request is greater than 150 kw, the 75 kw unit (unit 1) and the 150 kw unit (unit 2) split the load power corresponding to the fuzzy rules designed to approximate the optimal power distribution. FIG. 38 shows the total electrical efficiency by using this hybrid fuzzy rule-based PMS.

It can be seen that when the total load power request reaches 75 kw, the 75 kw unit (unit 1) ran full load, and the total electrical efficiency achieve its highest point. It is approximately 31%. When the total load power request reaches 150 kw, the 150 kw unit (unit 2) runs full load, and the system electrical efficiency achieve its third highest point. When the total load power request reaches 225 kw, both the 75 kw unit (unit 1) and the 150 kw unit (unit 2) run full load, and the system electrical efficiency achieve its second highest point. Identical units can find two or three identical highest efficiency points. This is not the case for different units because different units have different efficiency maps, and their maximum efficiency and the change of efficiency are different.

This system efficiency is satisfactory if compared with the optimal efficiency. This can be seen from FIG. 39 in the following page.

It can be seen that the system electrical efficiency of hybrid fuzzy rule-based implementation is almost exactly the same as that of optimal power distribution. This is the power distribution for one 75 kw unit and one 150 kw unit. The power distribution for three different units with two 75 kw units (unit 1 and unit 2) and one 150 kw unit (unit 3) will now be evaluated.

4.8.4. Three Different Units with Two 75 kw Units and One 150 kw Unit

For three different units, hybrid fuzzy rule-based implementation is used for power distribution in Matlab/Simulink according to the optimal power distribution results. FIG. 40 shows how the power management system split power among three different units with two 75 kw units and one 150 kw unit.

It can be seen that when the total load power request is less than 75 kw, only the 75 kw unit (unit 1) runs, and the other 75 kw unit (unit 2) and the 150 kw unit (unit 3) do not run. When the total load power request is greater than 75 kw and less than 150 kw, the two 75 kw units (unit 1 and unit 2) run the same load power and the 150 kw unit (unit 3) does not run. When the total load power request is greater than 150 kw and less than 225 kw, one 75 kw unit (unit 1) does not run, the other 75 kw unit (unit 2) and a 150 kw unit (unit 3) split the total load corresponding to the fuzzy rules designed to approximate the optimal power distribution. When the total load power request is greater than 225 kw, two 75 kw units run identical load power amount, and the power of the 150 kw unit corresponds to the fuzzy rules designed to approximate the optimal power distribution. FIG. 41 shows the total electrical efficiency by using this hybrid fuzzy rule-based power management system.

It can be seen that when the total load power request reaches 75 kw, the 75 kw unit (unit 1) ran full load, and the system electrical efficiency achieve its highest point. It is approximately 31%. When the total load power request reaches 150 kw, both 75 kw units (unit 1 and unit 2) run full load, and the system electrical efficiency also achieve its highest point. When the total load power request reaches 225 kw, the 75 kw unit (unit 1) does not run, the other 75 kw unit (unit 2) and a 150 kw unit (unit 3) run full load, and the system electrical efficiency achieve its third highest point. When the total load power request reaches 300 kw, all units run full load and the system electrical efficiency achieve its second highest point. For three identical units, there are three identical highest efficiency points as seen in FIG. 36. This is not the case for different units because different units have different efficiency maps, and different units have different maximum efficiency and different change of efficiency.

This system efficiency curve is satisfactory if compared with the optimal efficiency. This can be seen from FIG. 42.

From the graph, it can be seen that the hybrid fuzzy rule-based implementation approximates the optimal power distribution. This is the power distribution for two 75 kw units and one 150 kw unit. The power distribution for another combination, one 75 kw unit and two 150 kw units, will now be evaluated.

4.8.5. Three Different Units with One 75 kw Unit and Two 150 kw Units

FIG. 43 shows how the hybrid fuzzy rule-based power management system distributes power among three different units with one 75 kw unit (unit 1) and two 150 kw units (unit 2 and unit 3). All crisp rules and fuzzy rules used here are based on the optimal power distribution data.

From the graph, it can be seen that when the total load power request is less than 75 kw, only the 75 kw unit (unit 1) runs, and neither 150 kw unit (unit 2 and unit 3) runs. When the total load power request is greater than 75 kw and less than 150 kw, only one of the 150 kw units (unit 3) runs, and neither the 75 kw unit (unit 1) nor the other 150 kw unit (unit 2) run. When the total load power request is greater than 1501 cw and less than 225 kw, one of the 150 kw units (unit 3) does not run. The 75 kw unit (unit 1) and the other 150 kw unit (unit 2) split the total load corresponding to the fuzzy rules designed to approximate the optimal power distribution. When the total load power request is greater than 225 kw and less than 300 kw, the 75 kw unit (unit 1) does not run, and two 150 kw units (unit 2 and unit 3) equally split the total load power. When the total load power request is greater than 300 kw, two 150 kw units run identical load power amount; the load power is split between one 75 kw unit (unit 1) and the two 150 kw units (unit 2 and unit 3) corresponding to the fuzzy rules designed to approximate the optimal power distribution. FIG. 44 shows the total electrical efficiency by using this hybrid fuzzy rule-based power management system.

It can be seen that when the total load power request reaches 75 kw as shown in FIG. 44, the 75 kw unit (unit 1) runs full load, and the total electrical efficiency achieves its highest point, approximately 31%. When the total load power request reaches 150 kw, one of the 150 kw units (unit 3) runs full load and the system electrical efficiency achieves its fourth highest point. When the total load power request reaches 225 kw, the 75 kw unit (unit 1) and a 150 kw unit (unit 2) runs full load, and the system electrical efficiency achieves its second highest point. When total load power request reaches 300 kw, two 150 kw units (unit 2 and unit 3) run full load and the system electrical efficiency achieves its fourth highest point, which is the same system electrical efficiency as when the total load power request is 150 kw. When the total load power request reaches 375 kw, all units run full load and the system electrical efficiency achieves its third highest point.

The efficiency curve of the hybrid fuzzy rule-based system for one 75 kw unit and two 150 kw units also is satisfactory if compared with the optimal efficiency. It can be seen from FIG. 45.

From FIG. 45, it can be seen that the hybrid fuzzy rule-based implementation approximates the optimal power distribution.

4.9. Analysis of Results

The simulation results of the above five configurations in this chapter demonstrate that the performance of the proposed optimal rule-based and hybrid fuzzy rule-based PMS improve the system efficiency significantly compared to the rule-based PMS. That is currently used by our industry partner. These proposed PMS approximate the optimal results obtained by using the SQP method as described in Chapter 3. They are also easy to implement online.

5. Conclusion and Recommendations

5.1. Conclusion

In this Part, optimal power management strategies were designed for DG system with five configurations. First, SQP was used to find optimal power distribution for each configuration offline. Then the optimal system efficiencies were compared with that of existing power distribution methods. The simulation results shows that the optimal power distribution is much better than the existing power distribution methods. It can improve the system efficiency significantly. However, because of the time typically needed to calculate the optimal solution online by using mathematic methods such as SQP, rule-based and hybrid fuzzy rule-based systems were used to implement the optimal PMS according to the summary of the optimal data. The optimal solution results of some configurations have obvious patterns, around which rule-based PMS were designed. Some other configurations do not have obvious patterns in certain regions. In those cases hybrid fuzzy rule-based PMS were designed. The proposed rule-based and hybrid fuzzy rule-based PMS approximate the optimal power distribution. It is also easy to implement online.

5.2. Recommendations

GA can also be used to optimize the fuzzy systems. Alternatively, other evolutionary techniques such as particle swarm optimization (PSO) also can be used. Those evolutionary techniques can be used to tune fuzzy system parameters such as fuzzy membership functions and fuzzy rules.

The fuzzy system is powerful at exploring complex problems because it can be understood and built easily by engineers according to their experience since a fuzzy system encodes human reasoning. However, fuzzy logic lacks precision. Additionally, when the number of variables of a fuzzy system increases, the possible number of rules increases exponentially, and it will be difficult to design a complete rule set to achieve optimal system performance.

In the future, for the optimization part as described in Chapter 3, a DP also can be used to optimize the power distribution. DP is a global optimization method, and it can find the global optimizer directly. Additionally, engine start up cost can be taken into consideration when defining the system electrical efficiency cost function. For the implementation part as described in Chapter 4, the hybrid fuzzy rule-based systems still can be used to design PMS. However, look up tables also can be used to design the PMS if the environment is stable. The look up table is easy to implement online, though it is not robust against disturbance. In addition, the output of a look up table is generally more precise than the output of a fuzzy system if there is sufficient optimal data in the look up table.

No matter whether look up table or hybrid fuzzy rule-based PMS is used, in the future, it is better to take the site condition into consideration when designing those PMS. Generally speaking, when site conditions change, the engine efficiency map also changes. In this case, the “derate” table of the engine efficiency can be added into the PMS model to calculate the difference in performance based on the actual site conditions. And then to make the implementation results more practical and robust against environmental variation.

APPENDIX A TO PART 1

Optimization Programs A1 Two Identical Units diary eff6.txt clear all Pmax=75; for k=1:35 c(k)=k*2+5; Aeq=[1 1 ]; beq=c(k); lb=[0;0]; ub=[75;75]; if c(k)<=Pmax  y0=c(k)−5;  else   y0=c(k)/2+5;%c(k)/2+30 for n=2 end %for n=2;x0=[10;80];%[10;39];[20;40];[20;80];[30;48];[30;80];[40;60]; [40;70];[40;80] x0=[y0;c(k)−y0]; %x0=[0;12]; options = optimset(‘LargeScale’;off); [x,fval]=finincon(@myfun6,x0,[ ],[ ],Aeq,beq,lb,ub,[ ],options); x1 (k)=x(1); x2(k)=x(2); EFF(k)=c(k)/fval; end result=[c’ x1’ x2’ EFT] diary off --------------myfunction6 function f = rnyfun6(x) P=[10 14.7 20 23.3 30 40 50 60 70 80]; eff=[0.117 0.150 0.184 0.200 0.226 0.254 0.274 0.292 0.304 0.311]; n=2; format long p=polyfit(P,eff,n); f=(x(1)/poIyval(p,x(1))+x(2)/polyval(p,x(2))); A2 Three Identical Units diary eff7.txt Pmax=75; for k=1:70 c(k)=k*2+5; Aeq=[1 1 I]; beq=c(k); lb=[0;0;0]; ub=[Pmax;Pmax;Pmax]; if c(k)<=Pmax  yl=c(k)−5;  y2=2; elseif Pmax<c(k)<=2*Pmax   yl=c(k)/2+2;   y2=2; else  y 1 =c(k)/3+10;  y2=c(k)/3+10; end x0=[y 1 ;y2;c(k)−y1 −y2]; [x,fval]=finincon(@myfun7,x0,[ ],[ ],Acq,beq,lb,ub); x1(k)=x(1); x2(k)−−x(2); x3(k)=x(3); EFF(k)=c(k)/fval; end result=[c^(l) x1’ x2’ x3’ EFF’] diary off ----------myfun7---------- function f = myfun7(x) P=[10 14.7 20 23.3 30 40 50 60 70 80]; eff=[0.117 0.150 0.184 0.200 0.226 0.254 0.274 0.292 0.304 0.311]; n=2; format long p=polyfit(P,eff,n);   f=(x(1)/polyval(p,x(1))+x(2)/polyval(p,x(2))+x(3)/polyval(p,x(3))); A3 Two different Units diary eff8.txt clear all Pmax1=75; Pmax2=150; for k=1:215 c(k)=k*1+10; Aeq=[1 1 ]; beq = c(k) ; lb=[0;0;0]; ub=[Pmaxl;Pmax2]; if c(k)<=PmaxI  y0=c(k)−5;%or c(k)/2;if change to c(k)/4,the result will change elseif c(k)<=Pmax2   y0=2;%or 12 else    y0=c(k)/4;%or c(k)/3,or c(k)/3+40,c(k)/2 end x0=[y0;c(k)−y0]; [x,fval]=finincon(@myfun8,x0,[ ],[ ],Aeq,beq,lb,ub); xl (k)=x(1); x2(k)=x(2); EFF(k)=c(k)/fval; end result=[c’ x1’ x2’ EFF’] diary off -------------myfun8 function f= myfun8(x) P=[10 14.7 20 23.3 30 40 50 60 70 80]; eff[ 0.117 0.150 0.184 0.200 0.226 0.254 0.274 0.292 0.304 0.311]; P2=[20 30 40 60 80 90 100 120 140 150]; eff2=[0.1029 0.14 0.1699 0.2130 0.2410 0.2502 0.2605 0.279 0.2906 0.293]; n=2; format long p=polyfit(P,eff,n); q=polyfit(P2,eff2,n); f=(x(1)/polyval(p,x(1))+x(2)/polyval(q,x(2))); A4 Three Different Units with Two 751cw Units and One 150 kw Unit diary eff9.txt Pmax1=75; Pmax2=I50; for k=1:290 c(k)=k*1+10; Aeq=[I 1 1]; beq=c(k); lb=[0;0;0]; ub=[Pmax I ;Pmaxl ;Pmax2]; if c(k)<=Pmax 1 y1=c(k)−5; y2=2; elseif c(k)<=Pmax2 yl=c(k)/2+2; y2=c(k)/2+2; elseif c(k)<=Pmax2+Pmax1 y1=2; y2=c(k)13+10; else yl=c(k)/4; y2=c(k)/4; end x0=[y/;y2;c(k)−y1−y2]; [xfval]=fmincon(@myfim9,x0,0,[ ],Aerbbeq,lb,ub); xl(k)=x(1); x2(k)=x(2); x3(k)=x(3); EFF(k)=c(k)/fval; end result-lc’ xi’ x2’ x3’ EFF’] diary off -------------myfun9-------------------- function f = myfun9(x) P=[ 10 14.7 20 23.3 30 40 50 60 70 80]; eff=[ 0.117 0.150 0.184 0.200 0.226 0.254 0.274 0.292 0.304 0.311]; P2=[ 20 30 40 60 80 90 100 120 140 150]; eff2=[ 0.1029 0.14 0.1699 0.2130 0.2410 0.2502 0.2605 0.279 0.2906 0.293]; n=2; format long p=polyfit(P,eff,n); q=polyfit(P2,eff2,n); f=(x(1)/polyval(p,x(1))+x(2)/polyval(p,x(2))+x(3)/polyval(q,x(3))); A5 Three Different Units with One 75 kw Unit and Two 150 kw Units diary eff10.txt clear all Pmax1=75; Pmax2=150; for k=1:360 c(k)=k*1+10; Aeq=[1 1 1]; beq=c(k); 1b=[0;0;0]; ub=[Pmaxl ;Pmax2;Pmax2]; if c(k)<=Pmaxl yi=c(k)−5; y2=2; elseif c(k)<=Pmax2 y1=2 y2=2; elseif c(k)<=Pmax2+Pmaxl yl=c(k)/3; y2=2; elseif c(k)<=2*Pmax2 y1=2; y2=c(k)/2; else yl=c(k)/5; y2=c(k)/2;%or y2=2*c(k)/5 end x0=[yl ; y2; e(k)−yl−y2] ; [x,fval]=fmineon(@rnyfun10, x0, [ ], [ ],Aeq,be q, lb,ub); xl(k)=x(1); x2(k)=x(2); x3(k) =x(3); EFF(k)=e(k)/fval; end result=[c’ x1’ x2’ x3’ EPP] diary off   myfun10 function f = myfun10(x) P=[ 10 14.7 20 23.3 30 40 50 60 70 80]; eff=[ 0.117 0.150 0.184 0.200 0.226 0.254 0.274 0.292 0.304 0.31 I]; P2=[ 20 30 40 60 80 90 100 120 140 150]; eff2=[ 0.1029 0.14 0.1699 0.2130 0.2410 0.2502 0.2605 0.279 0.2906 0.293]; n=2; format Iong p=polyfit(P,eff,n); q=polyfit(P2,eff2,n); f=(x(1)/polyval(p,x(1))+x(2)/polyval(q,x(2))+x(3)/polyval(q,x(3)))

APPENDIX B TO PART 1

FIS Files B1 FIS of ELSE subsystem for Three Different Units with Two 75 kw Units and One 150 kw Unit [System] Name=13MS_5_3DIFF_25_2’ Type--‘mamdatur Version=2.0 Numlnputs=1 NumOutputs=1 NumRules=4 AndMethod=‘rrin’ OrMethod=‘max’ ImpMethod=‘min’ AggMethod-‘max. DefuzzMethod=’centroid’ [Inputl] Name-‘Total_Required_Power. Range-[223 300] NumMFs=4 MF1=1.2:1rapmf,[223 230 250.1944444444-44 258] MF2=‘M’I’trapmf,f254 262 280.342592592593 289] MF3=Th’Crapmf,[278.6 283.8 301A 314.6] MF4----’01C:trapmf,[248 254259.564814814815 265 [Outputl] Name--‘unit 3’ Range=[110 150] NumMFs=4 MF1=1;:lrapmf,[110.2 116.8 129.9 137.9] MF2=‘M’ftrapmf,[140.3 142.3 146.5 148.8] MF3-11‘..’trapmf,[146.1 1473 150 162.6] MF4-‘0K’ftrapmf,[134.7 137.6 141.8 144] [Rules] 1, 1 (1): 1 2, 2 (1): 1 3, 3 (1): 1 4, 4 (1): 1 B2 FIS of ELSE subsystem for Three Different Units with One 75 kw Unit and Two 150 kw Units [System] Name=‘PIV1S_5_3D1FF_2B_2’ Type=‘mamdani’ Version=2.0 NumInputs=I NumOutputs=1 NumRules=5 AndMethod−=min* OrMethod=‘max’ ImpMethod=‘min’ AggMethod=‘max’ DefuzzMethod=‘centroid. [Inputl] Name=‘Total Required_Power’ Range=[300 375] NumMFs=5 MF1=‘12:’trimf,[297.7 312.3 334.5] MF2=‘El’Atimf,[341.1 356.6 372.9] MF3=‘MYtriruf,[322.3 338.6 356.8] MF4=bk’ftrimf,[309.1 3253 341.4] MF5=VI-1*:*trimf,[359.1 366.6 376.8] [Outputl] Name=‘unit_1’ Range=[59 75] NumMFs=5 MF1=‘H’ftrirnf,[69.42 72.71 73.63] MF2=TH’:trimf,[73.2 74.54 77.18] MF3&L‘:’trimf,[58.52 62.88 67.2] MF4=‘M’Arimf,[65.85 70.3 70.92] MF5=‘0K’ftrimf’,[63.57 66.45 68.6] [Rules] 1, 3 (1) : 1 2, 1 (I) : 1 3, 4 (1): 1 4, 5 (I): 1 5, 2 (1) 10

Part 2—System Description

1. Introduction

One object of this design is to provide an integrated and optimized Distributed Generation System Control (DGSC) module that improves the overall power generation performance attributes and lowers the capital cost of a distributed generation site installation. The described embodiment leverages the IEEE 1547 “Standard for Interconnecting Distributed Resources with Electric Power Systems” (“Standard” herein) that has defined a nationally recognized standard for grid interconnect for distributed generation (DG) resources.

2. Top Level System Controller Description

2.1. Scope

This section outlines the characteristics of one embodiment of a top level system control of internal combustion engine generating system production units. Other types of generators and further variations of the specific design choices described herein will occur to those skilled in this technology area without undue experimentation based on this disclosure.

2.2. Applicable Documents

2.2.1. Standards

Commercial production components of the system may be selected to comply with the relevant aspects of IEEE 1547 and other standards listed below.

-   IEEE P1547 Standard for Distributed Resources Interconnected with     Electric Power System -   IEEE 519 IEEE Recommended Practices and Requirements for Harmonic     Control in Electric Power Systems -   UL 508C Standard for Power Conversion Equipment -   UL 2200 Stationary Engine Generators Assemblies -   NFPA 70 National Electric Code

2.2.2. Acronyms

DG Distributed Generator

DGSC Distributed Generator System Controller

HMI Human Machine Interface

GPM Grid Parallel Mode of operation

GIM Grid Isolated Mode of operation

I/O Input/Output

ISO International Organization for Standardization

UIC Utility Interface Controller

2.3. System Overview

2.3.1. System Definition

A DG unit is an internal combustion engine generating system with a synchronous generator. The DG system controller coordinates the control of one or more DG units as shown in FIG. 46. With the addition of hardware modules, the system controller shall be capable of controlling up to 8 parallel DG units that are connected to the local utility grid in GPM or to the local site distribution bus in GIM. The demonstration prototype will be capable of controlling 2 parallel units. Researchers will investigate the possibility of including DG units with induction generators.

2.3.2. DG Unit Description

The DG unit is a natural gas fueled engine driving a synchronous generator that produces 60 Hz three-phase electrical power at 277/480 VAC under ISO standard conditions. The rated output of each DG unit will be within the range 75-200 kW.

2.3.3 Software Coding

The preferred programming language for system control functions is C or C++, though many other computing languages would also be appropriate. Exceptions in various embodiments include relaying functions written in assembly language and monitoring software written with Microsoft Visual Basic.

2.3.4 Controller Structure and Communication

Each DG unit may include a subsystem control module. There are two main variations of the control structure presently under consideration.

Structure A involves DG subsystem modules communicating with a supervisory controller. The supervisory controller will perform the UIC functions as shown in FIG. 47.

Structure B involves DG subsystem modules communicating with each other and one module will assume the supervisory (i.e. master) control function. There will be an automatic procedure for determining which machine serves as the master. The user will also be able to specify a priority list for selecting the master unit. Within structure B there are two variants:

Structure B.1 has a separate UIC, somewhat similar to FIG. 47.

Structure B.2 incorporates UIC capabilities into every subsystem module.

Regardless of the structure, in these embodiments every subsystem module and any separate supervisory controller or UIC will be connected to a CAN bus network.

Regardless of the structure, in these embodiments every subsystem module and any separate supervisory controller or UIC will have an HMI.

Regardless of the structure, a password protected TCP/IP interface will allow a local or remote operator to monitor performance of the DG system and individual units. The TCP/IP interface will also allow the operator to upload and download system and individual unit control specification parameters interactively and in .xml file format.

There may also be dedicated analog and digital signal channels in addition to the CAN bus.

2.3.5 Control of Electrical Connections

Each DG unit shall be equipped with a motorized circuit breaker to interface with the site load bus. The DG system controller will also control the utility tie circuit breaker. The DG unit breaker and utility breaker control shall be governed according to the IEEE 1547 standard. Each DG unit shall be equipped with a fuel solenoid shutoff valve. The DG system controller will control the turning on and off of an additional fuel solenoid shutoff valve.

2.3.6 Import/Export Control

The generator set shall include provisions for controlling the amount of power that is imported from or exported to the utility grid.

TABLE 2-1 General characteristics of DG unit General characteristics Rated Output Power of Each DG Unit: 75 kW < P_(rated) < 200 kW AC Output Voltage: 3-phase, 277/480 VAC Output Frequency: 60 Hz Maximum Number of Units: 8 DG units Net Electric Efficiency at ISO at 75% Load 28% Base System Output for Pricing Purposes 480 V/60 Hz Power Factor Capability >0.8 Standard for Grid Interconnection IEEE 1547

2.4. DG System Controller Interface Descriptions

2.4.1 Human Machine Interface

Each DG unit and any supervisory controller in this embodiment is equipped with a Human Machine Interface (HMI) device to provide a local operator control panel, parameter settings, system indicators, visual alarm or shutdown information, and emergency power off. The HMI devices shall be able to display the following information: generator voltage and current, frequency, DG output in kw and kvar, oil pressure, water temperature, synchronization status, total kilowatt hours, and alarm history.

2.4.2. List of I/O for System Controller

Input switches in the preferred system controller include a run with load switch, mode selection switch (automatic mode or test mode), emergency stop switch, voltage raise/lower switch, and speed raise/lower switch. Utility switches include a “Utility source circuit breaker Aux in” input switch, “Utility source circuit breaker open/close” input switch, a “Utility/bus PT input” switch, a “Local bus PT disconnect,” and a “Mains PT disconnect” switch.

The generator portion of the system controller in this embodiment includes these inputs: “Generator circuit breaker Aux in,” “Generator circuit breaker open/close,” “Generator CT,” and “Generator PT.” Outputs are included for voltage bias and a Generator On/off Switch.

Engine-related I/O in this embodiment includes inputs for Engine warning, Engine fault, MPU pickup, Idle/rated speed, and Engine crank, as well as outputs for Speed bias, Fuel shutoff valve, and Engine On/off Switch.

2.5. Summary of System Functions

2.5.1 Summary of System Controller Functions

The system controller (DGSC) in the present embodiment provides several functions. At the system level, the DGSC provides grid synchronization and protection of the DG Unit, Regulation in GPM and GIM, and a human/automatic switch between GPM/GIM. Internally, the DGSC provides control of power to ENI auxiliary loads, provides gas shutoff valve control, monitors utility voltage, and implements lower-voltage power supply control. Further, the DGSC adds communication functionality in controlling the HMI, communicating with an external DG gateway, and controlling import and export of power.

2.5.2. Summary of UIC Functions

The UIC in the present embodiment complies with the IEEE 1547 Standard for Interconnecting Distributed Resources with Electric Power Systems.

2.5.3 Summary of DG Unit Protection Functions

The DG units in the present embodiment include current limit protection, emergency power shutdown, protective power shutdown, warning indications, generator over/under voltage indications, generator over/under frequency indications, anti-islanding protection, loss of mains detection, loss of generator excitation, speed/frequency mismatch protection, reverse power protection, and short circuit protection.

2.6 Mode of Operations and Regulations

2.6.1 Single Unit Configurations

Single units in the present embodiment may operate in GIM (voltage-regulating speed control mode) or GPM (voltage-following torque control mode).

2.6.2 Multiple Unit Configurations

Likewise, multiple-unit configurations of the present embodiment can also operate in GIM or GPM. In GIM, one unit uses voltage-regulating speed control, while other units use voltage-following torque control. In GPM, all units use voltage-following torque control.

2.6.3 Loss of Utility Power

In the event of a utility power outage, the DG system automatically disconnects from the utility and continues to provide power to the load. If the engines are not operating at the time of the outage, they start automatically, disconnect from the utility, and provide power to the load. Upon return of the utility power, the DG system synchronizes to the utility grid, reconnects to the utility, and continues as instructed prior to the outage.

2.6.4 Starting Parallel Units

In multi-unit operation, when a start command is sent to the DGSC, all units start and operate parallel to each other, then to the utility grid as needed to supply the load.

2.6.5.50/60 Hz Operation

The DG system is capable of operating at either 60 Hz or 50 Hz with a gearbox changes and appropriate electrical component changes.

2.6.6. Automatic and Manual/Test Modes

The DG system controller is capable of operating in either Manual/Test Mode or Automatic Mode.

2.6.7. Regulation in Grid Isolated Mode (GIM)

The total harmonic distortion of the DG system electrical output is less than 5% at no load. The DG system controller is capable of regulating the output voltage within a maximum range of +/−0.5% of nominal voltage in GIM (per ANSI84.1B). The DG system controller is capable of maintaining a maximum output voltage deviation of +20% to −25% given a 25% load pickup or a 100% load rejection in GIM. The frequency operating range of DG system in GIM is defined as +/−3% for 50 Hz or 60 Hz systems.

2.6.8 Regulation in Grid Parallel Mode (GPM)

The DGSC includes provisions for controlling the amount of power that is imported from or exported to the utility grid. The DGSC complies with the IEEE 1547 Standard for Interconnecting Distributed Resources with Electric Power Systems.

3. Modeling Overview

An integrated system model for the present embodiment was developed and validated in Matlab/Simulink. The modeling of the system included four major parts: engine, generator, load/grid, and system controller. Models for each individual component were developed and all of them were integrated into a system model.

3.1. Engine and Engine Control Module (ECM)

The engine model in this embodiment is a simplified inertia model based on the simple engine model illustrated in FIG. 48. The input parameter is the throttle angle command. The output parameter is engine torque generated and actual engine speed. The engine load torque is regarded as a disturbance to the engine system.

A quasi-static engine model (shown in FIG. 49) was applied in the simulation of the DG system because the engine operates at an approximately constant speed (e.g., at 1800 rpm).

The engine control module (ECM) is an independent control executing all of the engine management functions, including fuel/air ratio, governor, ignition and health monitoring. In the case of original engine speed closed-loop control, only a PID (or PI) feedback control was considered to maintain desired engine speed by controlling the engine throttle angle. It should be emphasized that the engine speed fluctuation should be kept to a minimum in order to achieve an expected grid frequency.

FIG. 50 shows a block diagram of the engine speed feedback control. By controlling the engine throttle angle, the engine speed can maintain a set point. For example, if the load torque increases suddenly for some reason, the engine speed will drop. Via feedback and PID controller, an engine speed drop will cause increase of the throttle angle. Therefore, more engine torque will be generated to make the engine speed return to a set point.

It should be noted that when engine is running at torque control mode, the output speed is not determined by the engine itself. The output speed will follow the speed in the grid. The system controller will monitor the output power and adjust the speed bias command to control the system.

3.2. Automatic Voltage Regulator (AVR) and Generator Module

3.2.1. Introduction to the AVR

The controller will send a command signal to the AVR to regulate the voltage. Because the present embodiment uses a brushless generator, the AVR cannot control the field voltage (V_(f)) directly. The field voltage (V_(f)) will be controlled through the exciter part. Therefore, the controller will control the exciter voltage (V_(r)) instead of the field voltage (V_(f)). The process of controlling voltage in the AVR starts from receiving the signal from controller and changing that signal to the exciter voltage (V_(r)). The exciter voltage (V_(r)) creates flux, which in this step, the process still happens in stator part, and this flux will create the field voltage from the rectifier, which is in the rotor part. The process of the system is shown in FIG. 51.

In the next step, we simplify the above system by using the relationship between the AVR and Generator in which we know as the graph of OCC (Open Circuit Condition). The relationship illustrated in FIG. 52 helps us to translate from exciter voltage (V_(r)) to internal voltage (Ea). Below, we show the simulation results from this graph. After that, we can calculate the terminal voltage (Vt) from the relationship between the output power, the armature reactance and the internal voltage assuming the power factor (PF) equals to 1. The formulas used to calculate the terminal voltage are derived from the phasor and schematic diagrams in FIG. 53:

$P = \frac{3\; V_{t}E_{a}\sin\;\delta}{X_{s}}$ V_(t) = E_(a)cos  δ − jX_(s)I_(a)sin  θ

3.2.2. AVR Model

We use the relationship above to generate the Simulink block diagram. As illustrated in FIG. 54, the input to the AVR is the error voltage signal from the controller. The output of the AVR and the input of the generator are the exciter voltage. And the output of the generator is the terminal voltage (V_(t)).

Instead of using the exciter and rectifier, we will use graph of OCC (Open Circuit Condition) to build the relationship. Then, we use close loop control with PID to build the model below.

In the example embodiment, the model of FIG. 55 takes 480V as the reference input value. After simulation with the step function of output power signal, we get the steady-state output at 480V also.

3.2.3. Simulation Results

The model that is shown in FIG. 56 is the AVR model by Matlab/Simulink program. This model is based on the model from FIG. 55.

The simulation results are shown in FIGS. 57 and 58. These figures illustrate the same data, but FIG. 55 is plotted with frequency 60 Hz. FIGS. 57-58 each include 3 graphs: Load Power (kw) vs. Time (s), Terminal Voltage (V) vs. Time (s) and Current (A) vs. Time (s).

For this simulation, we look closely at the effect of the terminal voltage (Vt) and current when the load power changes. We assume that the load power drops from 60 KW to 50 KW and suddenly increases from 50 KW to 60 KW at 6 and 12 seconds, respectively. And the figures show the changes of both voltage and current graphs.

3.3. System Controller Model

The list of system I/O for the system controller in this embodiment appears in Section 2.4 of this Part. The list of system functions appears in Section 3.3.2. In this example embodiment, most of those functions are implemented in a state machine.

3.3.1. PARAMETERS for the system controller

The parameters provided to the system controller in the present embodiment include: DG unit auxiliary load parameters, maximum current, maximum voltage, maximum engine speed, maximum load, maximum power, and maximum generator frequency.

3.3.2. System Function

There are two types of controllers in the system: DG Unit Controllers and one or more Supervisory Controllers. The former control a single DG unit while the latter coordinate the operation of multiple units in a single location or portion of a DG system.

DG Unit Controllers regulate the engine in GPM and GIM, control power to ENI auxiliary loads, control the gas shutoff valve, monitor utility voltage, control the lower voltage power supply, provide current limit protection, control emergency power shutdown and protective power shutdown, generate warning indications, detect and indicate generator over/under voltage and generator over/under frequency conditions, provide anti-islanding protection and loss of mains detection, detect and indicate loss of generator excitation and speed/frequency mismatch, provide reverse power protection, detect and indicate short circuit conditions, and control the unit's import and export of power.

The Supervisory Controller controls grid synchronization and protection of the DG Unit, provides a human/automatic switch between GPM/GIM, controls the HMI, and communicates with an external DG Gateway. The UIC Controller complies with the IEEE 1547 Standard for Interconnecting Distributed Resources with Electric Power Systems.

3.3.3. GPM/GIM Mode Regulation

The DG system can run at GIM mode or GPM mode. Each DG unit will be running at either speed control mode or torque control mode according to the situation. The supervisory controller will determine the control mode of each DG unit. The basic rules are as follows

TABLE 3-1 Control mode rules in GIM and GPM mode GIM GPM Single DG unit speed control torque control Multiple DG units one master unit uses speed control, all units use other units use voltage-following torque control torque control

When running in speed control mode, the DG unit controller will send out constant speed bias commands to the Engine Control Module (ECM). The constant speed bias will be 1800 rpm (translated from 60 Hz frequency). The DG unit controller also sends out constant voltage bias commands to the Automatic Voltage Regulator (AVR).

When running in torque control mode, DG unit controller will monitor the output power of DG unit and adjust the speed bias command to control the output torque. The speed bias command sent to the ECM would change the output torque instead of the speed of the engine. The engine speed will follow the grid speed automatically. DG unit controller also sends out voltage bias commands, which are the same as the grid voltage, to the Automatic Voltage Regulator (AVR).

3.3.4. Feed-Forward Controller in GIM Mode

It can be seen from FIG. 50 that, by controlling the engine throttle angle, the engine speed can be maintained at a set point. For example, if the load torque increases suddenly for some reason, the engine speed will drop. Via feedback and PID controller, an engine speed drop will cause an increase of the throttle angle. Therefore, more engine torque will be generated to make the engine speed return to a set point.

It can be also seen from the FIG. 50 that the engine speed definitely drops when the load torque increases suddenly no matter how the PID controller was designed. That is, an engine speed bias was sensed firstly, and then the PID controller takes effect to maintain the engine speed. The simulation results (as shown in FIG. 59) prove that the engine speed is subject to the changing load torques when only a feedback control is used.

Combined feed-forward plus feedback control is proposed to reduce the effect of the measurable disturbance (such as load torque) on the engine speed output. In the most ideal situation, feed-forward control can entirely eliminate the effect of the measurable disturbance on the engine speed output. Even when there are modeling errors, feed-forward control can often reduce the effect of the measurable disturbance on the output better than that achievable by feedback control alone.

In the DG system, the engine load torque can be calculated based on the local consumed power and the amount of power that is imported from or exported to the utility grid. FIG. 60 gives the block diagram of a feed-forward plus feedback engine speed control system considering the engine torque is a measurable disturbance.

In FIG. 60, the load torque can be calculated by the summary of various load powers. Therefore, the engine load torque can be regarded as a measurable signal, rather than a disturbance signal.

FIG. 61 gives the simulation results of the feed-forward plus feedback engine control system. It can be seen that feed-forward control is able to rapidly suppress the changes of the engine load torque. For example, if the load torque increases suddenly for some reason, the feed-forward control goes into action and the throttle angle will increase immediately even without engine speed drop. The engine speed is robust against the changing engine load torque. Therefore, the engine speed fluctuation is little subject to the changing engine load torque via feed-forward control.

3.3.5. Engine Control in GPM Mode

When considering the problem of frequency control of interconnected areas, we assume that the utility grid is an infinite power pool. That is, the generator cannot change the grid frequency. The following block diagram gives the power flows among the generator, various loads and tie-line and also gives the phasor diagram for the generator and utility grid.

In FIG. 62, we can obtain the formula for the real (not including reactive) generator power, as follows:

$P_{G} = {{P_{L} - P_{U}} = {\frac{{E}{{Vt}}}{X}\sin\;\delta}}$ where the angle δ is the phase angle between the generator emf E and the utility voltage Vt. Here the power angle δ is defined positive when E leads Vt; P_(G), P_(L), P_(U), are the real power of the generator, various loads and utility grid respectively.

In the present embodiments, before the generator is connected with the grid, the two are synchronized. Synchronization can take place if the following conditions are all satisfied:

1. The generator and grid frequencies are equal.

2. The phase sequence of the generator matches that of the grid.

3. The generator emf E and the grid voltage U are of equal magnitude.

4. E and U have equal phase.

If and only if all these conditions are satisfied, the voltage across the circuit breaker 52G1 and 52-1 is zero. At this time, the generator can be smoothly “locked” onto the grid by closing the circuit breakers.

Once the synchronous generator is synchronized onto the grid network, its speed will always synchronize with the grid frequency as long as the grid power is large enough. That is, the speed of the engine coupling with the generator cannot be changed either.

It can be observed that the magnitude and direction of the power flow of the machine will be determined according to the power angle δ. In reality, the power angle δ is controlled by means of the engine torque (or engine power). If the engine produces more power than consumed by various loads, the rest of the power will flow to the grid.

To sum up, when DG units are interconnected with the grid, though the engine speed cannot be changed by the throttle, the throttle can still control the engine torque (or engine power) so as to control the power flow between the generator and the tie-line. FIG. 63 gives the block diagram of the feed-forward control for maintaining a minimum import power from the grid.

The engine speed controller (inner PID) accepts an engine speed bias as an input, but the engine speed is completely determined by the grid. So if we set the engine speed bias equal to 5 rpm and the synchronous engine speed is actually 1800 rpm, then engine speed controller might tell the engine we want to run at 1805 rpm. Then the engine would try harder, thus increasing power, but would still turn at grid synchronous speed 1800 rpm.

The outer PID controller monitors the grid power (or generator output power minus load power) in load-following mode to determine the engine speed bias sent to the engine speed controller (inner PID). As mentioned above, the inner PID can control the engine torque (or engine power) output, thus controlling the amount of the power imported from the grid indirectly.

Assuming the minimum import power in the utility contract is 10 kW, the simulation results (shown in FIG. 64) show how the outer PID controller works to maintain 10 kW import power.

3.4. Load/Grid Module

The grid is modeled as a voltage source and impedance, while the load is modeled as an impedance. The input parameters for the load/grid are the impedance of the grid, the working voltage of the grid, the maximum voltage of the grid, and the impedance of the load.

3.5. Islanding Detection

The dynamic model of a DG connected to the grid resembles that of a network containing one small generator connected by a distribution line to a much larger generator. The small generator represents the DG and the large generator represents the grid. All the synchronous generators in a power system operate in lock step synchronism because the AC voltage results in synchronization of torques between the machines. Therefore, all machines in an interconnection have nearly identical average frequencies. However, there can still be differences in the instantaneous frequencies of interconnected machines. The present islanding-detection scheme uses the fact that deviations in frequency caused by a deliberate perturbation signal are much smaller when a DG is connected to the grid than when it is in an island.

The circuit diagram in FIG. 65 shows the classical model of two synchronous generators connected by a distribution line. The voltage source in series with reactance jx₂ on the right hand side represents the DG unit synchronous generator. Resistance R₂ represents a load that matches the DG real power output. The corresponding elements on the left hand side of the diagram represent a generator having 100 times the inertia of the DG along with its matching load. Reactance jx_(L) represents a power distribution line. Islanding is simulated by disconnecting the distribution line.

FIG. 66 shows simulated frequency measurements from the DG unit before and after the distribution line is disconnected. A 1 Hz perturbation signal is superimposed on the DG unit's throttle signal during the entire simulation. The perturbation signal produces a 1% variation of the DG mechanical input power. The horizontal axis indicates measurement samples that have a frequency of 720 Hz. Disconnection of the distribution line occurs after 5 seconds (3600 samples). Measurement noise has been simulated by adding actual frequency data from a PMU. Frequency deviations caused by the perturbation signal are almost completely obscured by noise before the DG and its matching load become an island. The 1 Hz frequency deviation is easily observed after the distribution line between the two machines is removed.

FIG. 67 shows the magnitude of the 1 Hz component of the signal in FIG. 66. This simulation shows that a simple threshold test of this magnitude should work as the islanding detection algorithm.

After the DGSC has been modified to inject a 1 Hz perturbation signal into the throttle of a synchronous DG unit, experimentation, simulations and analysis can be carried out to determine appropriate thresholds for the algorithm. Research on such details of the algorithm will proceed in parallel with most of the engineering tasks. Ultimately, the supervisory controller will be programmed to determine an appropriate setting for the threshold test depending on the number and type of DG units connected in parallel. The island-detection scheme will be validated in the test cells at I Power according to the IEEE 1547 conformance test procedures. Possible additional variations in an island configuration, such as off-site DG units connected to the same feeder, will be studied in simulation to determine whether any additional logic is required.

4. Utility Interface Controller (UIC)

IEEE Standard 1547, “Standard for Interconnecting Distributed Resources with Electric Power Systems”, provides for the first time a nationally recognized set of rules for connecting distributed generation (DG) resources to a utility grid. This standard has the potential to be used by federal legislators, by state public utilities commissions, and by over 3000 utilities in formulating technical requirements for grid interconnection of DG. This standard specifies requirements for synchronization, protective relaying, and switching coordination that were formerly determined on a utility-by-utility basis.

There is a large amount of redundancy between the basic functions used in DG operation and those required for compliance with the IEEE 1547 standard. Both require and/or can be partially met through the proper use of over/under voltage relays, over/under frequency relays, fault current detection relays, and synchronization check relays. The following section summarizes aspects of the UIC specification for use in many embodiments of this system.

4.1. Partial Summary of IEEE 1547 Standard

4.1.1 Synchronization

The Standard states that the DR must synchronize with the EPS without causing a voltage magnitude fluctuation at the Point of Common Coupling (PCC) greater than ±5% of the operating voltage. PCC is defined as “the electrical connecting point or interface between the utility distribution system and the customer's or user's electrical distribution system.”

The output of the DR and the input of the EPS at the PCC have substantially the same voltage magnitude, the same frequency, and the same phase angle. IEEE Standard 1547 requires that the difference between the voltage of the distributed generator and the EPS not be more than 10%, the difference between their frequencies not exceed 0.3%, and the difference between their phase angles not exceed 20°. Only if these conditions are satisfied can the distributed generator be connected into the electric power system. The following table illustrates the requirements of the Standard.

TABLE 4-1 IEEE 1547 Requirements and conditions Aggregate Rating of Frequency Voltage Phase Angle DR Units Difference Difference Difference (kVA) (Δf, Hz) (ΔV, %) (Δø, °)  0-500 0.3 10 20   500-1,500 0.2 5 15  1,500-10,000 0.1 3 10

In order to adhere to this requirement, we can use relays to estimate the magnitudes and phase angles of the voltages, and frequencies on the DR side and the EPS side. It can then be checked if the differences between the estimations are within the ranges mentioned above. If they exceed the mentioned values then the DR will not be connected to the EPS. In order to ensure that the distributed resource will synchronize with the EPS with a voltage fluctuation limited to ±5% of the operating voltage, we can carry out the test by connecting the DR to the EPS a couple of times and checking if the voltage fluctuation is within ±5% of the operating voltage.

4.1.2. Inadvertent Energizing of Area EPS

The Standard states that the distributed resource must not connect to the PCC if the Area EPS is in the de-energizing state. It also states that the distributed resource must not connect to the PCC until the voltage of the EPS is in the range of 106V-132V and the frequency is in the range of 59.3 Hz to 60.5 Hz. After the EPS has regained the normal voltage and frequency, the Standard requires that the distributed resource wait for up to 5 minutes before it reconnects to the EPS. The following table illustrates this requirement and conditions.

TABLE 4-2 EPS status and conditions Whether the DR is connected to the PCC EPS Status and Conditions Not connected EPS in a deenergized state. Connected EPS in a normal state: 106 V < V < 132 V and 59.3 Hz < f < 60.5 Hz. Not connected EPS in an abnormal state: V ≦ 106 V or V ≧ 132 V or f ≦ 59.3 Hz or f ≧ 60.5 Hz Connected with a 5-minute delay EPS recovered from an abnormal state to a normal one. This requirement may be satisfied by each time checking the voltage magnitude and frequency of the EPS after the occurrence of an outage. We can then compare these values obtained with the above mentioned threshold limits. If they are within the limits then wait for 5 minutes and then check again the voltage and frequency values. If they are still within the limits then close the circuit breaker between the DR and the EPS else keep the circuit breaker open and carry out the same procedure until the condition is satisfied.

4.1.3. Voltage Disturbances

The standard states that the protective functions of the interconnection system must measure the fundamental frequency component of the phase to phase or the phase to neutral voltage. If the measured quantity is less than/equal to 106V or greater than/equal to 132V then the distributed resource must stop energizing the EPS within the clearing times as indicated in the table below.

TABLE 4-3 Voltage clearing times per IEEE 1547 Voltage range (V) Clearing times (sec) V < 60 0.16  60 < V < 106 2 132 < V < 144 1 144 < V 0.16

Voltage disturbances bring about a change in the voltage of the power system. Relays can be used to check the voltage at the PCC. Whenever the voltage goes beyond the limits mentioned, the Standard requires that the relays disconnect the DR from the EPS within the respective clearing times as mentioned in the table above.

4.1.4. Frequency Disturbances

The Standard states that the protective functions of the interconnection system must measure the frequency. If the measured frequency goes out of the normal range (59.3 Hz<f<60.5 Hz) then the distributed resource must stop energizing the EPS within the clearing times as indicated in the table below.

TABLE 4-4 Frequency disturbances requirements DR “Cease to DR Size EPS Frequency Energize” Time ≦30 kW >60.5 Hz .16 sec. <59.3 Hz .16 sec. >30 kw >60.5 Hz .16 sec. 59.3-57.0 Hz Time Delayed <57.0 Hz .16 sec.

Frequency disturbances bring about a change in the frequency of the power system. Over-/under-frequency relays can be used to check the frequency at the PCC. Whenever the frequency goes beyond the limits mentioned, the relays must disconnect the DR from the EPS within the respective clearing times as mentioned in the table above. Note that DR units with a total capacity larger than 30 kW can have an impact on distribution system security. Thus, the IEEE 1547 requirement leaves this question to the Area EPS operator who specifies the frequency setting and time delay for under-frequency trips down to 57 Hz.

4.1.5. Disconnection of Faults

The Standard states that the distributed resource must disconnect from the area EPS for faults on the area EPS it is connected to. It requires the DR to have a current based protection and a ground fault protection suitable for detection of area EPS faults.

To provide current based protection, over current relays following the inverse definite minimum type (I.D.M.T.) characteristics will be used. The trip and reset characteristics of the over current relay is as shown in FIG. 68.

The time taken by the relay to operate depends on the torque, which in turn varies with respect to the current in the relay coil. The more torque, the less time taken by the relay to operate. Hence the relay is said to have inverse time characteristics.

In order to emulate an induction-type over-current relay, the various phenomena occurring in an induction disk of the electromagnetic relay can be represented in terms of mathematical equations. The equations used to simulate the trip and reset characteristics are as follows: T _(r) =TD(R/|M ²−1)--------------------→for 0<M<1---→Reset characteristic T _(r) =TD(A/(M ^(P) −C)+B)+K---------------→for M>1--------→Trip Characteristic Where: M=Multiple of PICKUP setting (0 to 40) T_(t)=Time to trip when M≧1 T_(r)=Time to reset if relay is set for integrating reset when M<1. Otherwise, reset is 50 milliseconds or less TD=TIME DIAL setting (0.0 to 9.9) A, B, C, p, K=Constants for the particular curve R=Constant defining the reset time.

4.1.6. Implementation Using Matlab Code

The source code is attached in Appendix A.

4.2. Phasor Estimation Methods

In phasor estimation we want to find the fundamental frequency sinusoid that best represents a set of measurement samples. We can estimate phasors using either least squares or orthogonal projection methods. Both methods give the same result when orthogonal vectors are used to represent the sample data. The orthogonal projection method is perhaps more intuitive and is explained in more detail below.

4.2.1. Orthogonal Projection Method

The orthogonal projection of a vector V onto the span of {V₁, V₂} is given by

$V_{est} = {\frac{{< V},{V_{1} > V_{1}}}{{V_{1}}^{2}} + \frac{{< V},{V_{2} > V_{2}}}{{V_{2}}^{2}}}$ where < > represents inner product of vectors. Orthogonal projection gives closest vector in the span of {V₁, V₂} to V.

With K samples of data per fundamental frequency period, we use the following vectors V ₁(L)=[cos((L−K+1)θ)cos((L−K+2)θ) . . . cos(Lθ)] V ₂(L)=[sin((L−K+1)θ)sin((L−K+2)θ) . . . sin(Lθ)] to approximate the most recent vector of samples V(L)=[y _(L−K+1) y _(L−K+2) . . . y _(L)] where θ=2π/K=ω₀ Δt, ω₀ is the nominal fundamental frequency, and Δt is the sampling interval. Then Vest(L)=[A cos((L−K+1)θ+φ)A cos((L−K+2)θ+φ) . . . A cos(Lθ+φ)] is the best fundamental frequency sinusoidal approximation to the vector of samples, where the following expressions correspond with the most recent window of measurements:

${A = \sqrt{Y_{c}^{2} + Y_{s}^{2}}},{\varphi = {{\tan^{- 1}\left( {- \frac{Y_{s}}{Y_{c}}} \right)} + {0.5\;{\pi\left( {1 - {{sign}\left( Y_{c} \right)}} \right)}}}}$ ${Y_{c =}\frac{{< V},{V_{1} >}}{{V_{1}}^{2}}},{Y_{s =}{\frac{{< V},{V_{2} >}}{{V_{2}}^{2}}.}}$

Therefore Ae^(jφ)(L) is the phasor estimate for the signal after sample L is received. The calculation is equivalent to the Discrete Fourier Transform with an assumed fundamental frequency equal to the nominal power system frequency ω₀. The actual power system frequency can be estimated from the rate of rotation of the calculated phasors: f(L)=[φ(L)−φ(L−1)]/(2πΔT) Averaging a few successive f(L) estimates is sufficient for filtering out the noise that is amplified by the derivative calculation.

4.2.2 Recursive Calculation of Phasors

Recursive forms of Fourier algorithms are used to reduce the number of calculations compared with the non-recursive Fourier algorithm. For a full-cycle window (Kƒ=2π): Ŷ _(c) ^((new)) =Ŷ _(c) ^((old)) +[y _(new) −y _(old)] cos(Lθ) Ŷ _(s) ^((new)) =Ŷ _(c) ^((old)) +[y _(new) −y _(old)] sin(Lθ) where y_(new) is the newest sample corresponding to L and y_(old) is the oldest sample corresponding to a full cycle earlier.

4.2.3. Least Squares Formulation and the Transient Monitor Function

When the data window spans the instant of fault inception, the results obtained from almost any algorithm are unreliable as the data contains both pre-fault and post-fault samples. The least squares formulation of the sinusoidal estimate is convenient for calculating the error between the samples and the estimate. The sample values corresponding to the phasor estimate can be calculated as: ŷ(L)=S(S ^(T) S)⁻¹ S ^(T) y(L) where S is a matrix with two columns: V₁(L)^(T) and V₂(L)^(T). The reason L is not shown in the expression involving S is that the matrix S (S^(T)S)⁻¹S^(T) turns out to be independent of L. The residual error vector is calculated as: r(L)=ŷ(L)−y(L)=[S(S ^(T) S)⁻¹ S ^(T) −I]y(L)=My(L) The sum of the absolute values of the elements of r(L) is defined as the transient monitor function. A recursive calculation can also be derived for the residual error vector.

4.3. Application of Symmetrical Component Calculations

A fault causes unbalanced current and voltages in the phases of a polyphase circuit. Three unbalanced phasors of a three-phase system can be resolved into three balanced system of phasors and are called symmetrical components of unsymmetrical phasors. The balanced sets of components are:

-   -   1. Positive-sequence components consisting of three phasors         equal in magnitude, displaced from each other by 120° in phase         and having the same phase sequence as original phasors.     -   2. Negative-sequence components consisting of three phasors         equal in magnitude, displaced from each other by 120° in phase         and having the phase sequence opposite to that of original         phasors.     -   3. Zero-sequence components consisting of three phasors equal in         magnitude and with zero displacement from each other.         V _(a) =V _(a) ⁽⁰⁾ +V _(a) ⁽¹⁾ +V _(a) ⁽²⁾         V _(b) =V _(b) ⁽⁰⁾ +V _(b) ⁽¹⁾ +V _(b) ⁽²⁾         V _(c) =V _(c) ⁽⁰⁾ +V _(c) ⁽¹⁾ +V _(c) ⁽²⁾         In matrix form: (a=1∠120°)

$\begin{matrix} {\begin{bmatrix} V_{a} \\ V_{b} \\ V_{c} \end{bmatrix} = {\begin{bmatrix} 1 & 1 & 1 \\ 1 & a^{2} & a \\ 1 & a & a^{2} \end{bmatrix}\begin{bmatrix} V_{a}^{(0)} \\ V_{a}^{(1)} \\ V_{a}^{(2)} \end{bmatrix}}} \\ {= {A\begin{bmatrix} V_{a}^{(0)} \\ V_{a}^{(1)} \\ V_{a}^{(2)} \end{bmatrix}}} \end{matrix}$ In matrix form:

$\begin{matrix} {\begin{bmatrix} V_{a}^{(0)} \\ V_{a}^{(1)} \\ V_{a}^{(2)} \end{bmatrix} = {{\frac{1}{3}\begin{bmatrix} 1 & 1 & 1 \\ 1 & a & a^{2} \\ 1 & a^{2} & a \end{bmatrix}}\begin{bmatrix} V_{a} \\ V_{b} \\ V_{c} \end{bmatrix}}} \\ {= {A^{- 1}\begin{bmatrix} V_{a} \\ V_{b} \\ V_{c} \end{bmatrix}}} \end{matrix}$ Zero sequence components are never present in line voltages regardless of the degree of unbalance because the sum of line-to-line voltage phasors in a three-phase system is always zero.

Line currents into a delta connected circuit have no zero-sequence currents. For a delta circuit: I _(a) ⁽¹⁾=(1−a)I _(ab) ⁽¹⁾ I _(a) ⁽²⁾=(1−a ²)I _(ab) ⁽²⁾ Line-to-line voltages in a star connected circuit have no zero-sequence components. For a star circuit: V _(ab) ⁽¹⁾=(1−a ²)V _(an) ⁽¹⁾ V _(ab) ⁽²⁾=(1−a)V _(an) ⁽²⁾ In the absence of a neutral connection, zero-sequence currents are not present. Also, there cannot be any positive or negative sequence currents in the connections from neutral to ground.

Sequence networks are developed for various components of a power system like transmission line, transformer or synchronous machine based on these symmetrical components.

4.3.1. SCDFT: Symmetrical Component Discrete Fourier Transform

The computational burden associated with the computation of the symmetrical components can be greatly reduced by the choice of sampling frequency. If the sampling frequencies that correspond to θ=30°, 60°, or 120° are used then the DFT and the symmetrical component calculation can be effectively combined. If θ=30° and Δ y_(L)=[y_(new)−y_(old)] (for full cycle algorithm) we can produce full-cycle SCFDT with these expressions: Y _(oc) ^((L+1)) =Y _(oc) ^((L))+(Δy _(a,L) +Δy _(b,L) +Δy _(c,L))cos(Lθ) Y _(os) ^((L+1)) =Y _(os) ^((L))+(Δy _(a,L) +Δy _(b,L) +Δy _(c,L))sin(Lθ) Y _(1c) ^((L+1)) =Y _(1c) ^((L)) +Δy _(a,L) cos(Lθ)+Δy _(b,L) cos(L−4)θ+Δy _(c,L) cos(L+4)θ Y _(1s) ^((L+1)) =Y _(1s) ^((L)) +Δy _(a,L) sin(Lθ)+Δy _(b,L) sin(L−4)θ+Δy _(c,L) sin(L+4)θ Y _(2c) ^((L+1)) =Y _(2c) ^((L)) +Δy _(a,L) cos(Lθ)+Δy _(b,L) cos(L+4)θ+Δy _(c,L) cos(L−4)θ Y _(2s) ^((L+1)) =Y _(2s) ^((L)) +Δy _(a,L) sin(Lθ)+Δy _(b,L) sin(L+4)θ+Δy _(c,L) sin(L−4)θ

4.3.2 Power in Terms of Symmetrical Components

The total complex power (in volt-amperes) flowing into a three-phase circuit through the lines a, b and c is: S _(3Φ) =P+jQ=V _(a) I _(a) *+V _(b) I _(b) *+V _(c) I _(c)*=3V _(a) ⁽⁰⁾ I _(a) ⁽⁰⁾*+3V _(a) ⁽¹⁾ *I _(a) ⁽¹⁾*+3V _(a) ⁽²⁾ I _(a) ⁽²⁾* The transformation of a-b-c voltages and currents to symmetrical components is power-invariant.

4.3.3 Symmetrical Component Distance Relay

The use of phasor calculations permits the use of symmetrical components in the detection of fault type and distance. For all possible fault types a general expression for the fractional distance to the fault is:

$k = \frac{k_{1} + {k_{2}k_{2}^{\prime}} + {k_{0}k_{0}^{\prime}}}{1 + k_{0}^{\prime} + k_{2}^{\prime} + k_{1}}$ where all the quantities k (see FIG. 69) can be calculated from the symmetrical components of the voltage and current phasors at one end of the transmission line.

4.4. UIC Algorithm Development

4.4.1. Problem Description

The schematic in FIG. 70 shows a typical structure of Gensets and UICs. Up to 8 distributed generation Gensets each via a circuit breaker (CB) are connected to a local bus. The functionality of a UIC is implemented in two modules, namely, Phasor Measure Unit (PMU) module and Main Utility Interface Controller (Main UIC or simply UIC) module.

Each CB in this embodiment is equipped with a PMU that implements the following functions:

-   -   Checking the status of the CB, e.g., determining if the CB is         open or closed;     -   Sampling 3-phase currents flowing in the CB;     -   Sampling 3-phase voltages on both terminal sides;     -   Calculating current and voltage phasors;     -   Calculating frequencies on both terminal sides;     -   Buffering calculation results;     -   Communicating with Main UICs and sending results to them.

The Main UIC, an integrated part of the DG Genset controller, is helpful in many embodiments that are designed to satisfy the requirements of IEEE 1547. In the present embodiment, it implements the following two kinds of functions:

Slave functions:

-   -   Communicating with PMUs and retrieving current phasors, voltage         phasors, frequencies, and CB statuses;     -   Sending commands to break/make the CB that is directly connected         to the Genset controlled by its integrated DG controller; and     -   Receiving commands from the UIC performed as the master and         executing the commands;         Master functions:     -   Communicating with PMUs and retrieving current phasors, voltage         phasors, frequencies, and CB statuses;     -   Sending commands to break/make the CB that is directly connected         to the Genset controlled by its integrated DG controller;     -   Sending commands to other UICs performed as slaves;     -   Performing under-/over-voltage protection;     -   Performing under-/over-frequency protection;     -   Performing fault detection and protection;     -   Timing synchronization and changing operation mode from isolated         to parallel;     -   Detecting loss of synchronism and changing operation mode from         parallel to isolated;     -   Performing other relaying functions required by IEEE 1547.         The communication protocol among Main UICs and PMUs is a CAN         bus.

4.4.2. Inputs and Outputs

Input signals to UIC include the following:

-   -   3-phase currents, provided by Current Transformers (CTs),         flowing through each CB;     -   3-phase voltages, provided by Potential Transformers (PTs),         appearing on both terminal sides of each CB;     -   Status of each CB.         Output signals from UIC include the following:     -   Break/Make signals to CBs;     -   Values need to be sent the human machine interface (HMI) or         human computer interface (HCI) including currents, voltages,         frequencies, etc.

4.4.3. Programming Languages

Algorithms run on PMUs will be coded in PIC assembly language. Algorithms run on Main UICs will be coded in high level programming language, such as C, Matlab, etc.

4.4.4. Logic Flow

The PMU's main logic flow is illustrated in the flowchart in FIG. 71.

5. Prototype Design

5.1. System Controller Design

Illustrated in context as a block diagram in FIG. 72, the controller system consists of a number of PMUs (Phasor Measurement Unit) and a mainstream desktop computer with a PCI CAN card and a PCI I/O card. The PC will be the workhorse of the controller that undertakes all computing tasks of UIC (Utility Interface Controller) and the system controller. A PMU acts as a digital sensor that measures 3-phase currents or voltages. The PCI CAN card has two ports. One port is for local communications with PMUs in the same DG unit. The other is for communications between DG units as well as communications between DG unit and PMUs at Common Coupling Point (CCP). The PCI I/O card takes care of all other local inputs, such as oil pressure, and outputs, such as speed bias to Engine Control Module (ECM).

This exemplary embodiment of the hardware includes: 3.0 GHz, Pentium 4 processor with 800 MHz front side bus; 1 GB DDR2 RAM; 300 GB, 7200 rpm, 8 MB buffer SATA hard drive; 16×, double layer DVD±R/RW drive; 4 available PCI slots; 1 serial port, 1 parallel port, and 1 LAN port; 2 USB ports; Integrated audio and video; and 19-inch digital LCD. The PC's software in this embodiment includes: MS Windows XP Professional with SP2; MS Visual Studio .NET; and the Math Works Matlab with Simulink and an appropriate collection of toolboxes as will occur to those skilled in the art. Example PC hardware systems include DELL OPTIPLEX GX520 and the HP Compaq Business Desktop 5000 series.

CAN Cards in this embodiment use a PCI interface, provide 2 separate ports for data exchange, and a Windows DLL library. For example, the Advantech PCI-1680U-A: 2-Port CAN Interface Universal PCI Communication Card with Isolation works well.

The I/O Cards in this embodiment preferably have the following characteristics: A/D sampling rate of 720 samples per second per channel; A/D sampling resolution of 12-bit A/D converter; 3 A/D input channels; 16 digital input channels; 12 digital output channels; D/A resolution of 12-bit D/A converter; 2 D/A output channels; and a corresponding Windows DLL library. In various embodiments, these I/O Cards include Advantech PCI-1710-B 100 KS/s, 12-bit High-gain PCI-bus Multifunction DAS Card; Advantech PCLD-8710-A Wiring Terminal Board for PCI-1710/1710HG; and/or Advantech PCL-10168 68-Pin SCSI Cable, 1 m.

The connection between EGCP-2's Inputs and Outputs and the PC-Based Controller's Inputs and Outputs in this embodiment as follows:

TABLE 5-1 PC-based solution wiring diagram PC-Based Controller EGCP-2 # of I/O A/D Description Location Counterpart units I A Input Power 1-2 N/A I A PT Inputs 40-48 PMUs + CAN card port 4 + 1 I A CT Inputs 89-94 PMUs + CAN card port 2 + 1 I A MPU (Speed) 70-72 A/D channel on I/O card 1 I A Process 86-88 N/A I A Coolant Temp 66-67 A/D channel on I/O card 1 I A Oil Pressure 68-69 A/D channel on I/O card 1 O A Speed Bias 73-75 D/A channel on I/O card 1 O A Voltage Bias 37-39 D/A channel on I/O card 1 I D Discrete Inputs 49-65 Digital input channel 16 O D Relay Outputs  5-35 Digital output channel 12 I/O D RS-485 76-80 CAN card port 1 I/O D RS-422 81-85 N/A

5.2. System Controller Design

5.2.1 System Structure

The system controller includes following function modules

-   -   Supervisory control functions     -   DG Unit control functions     -   UIC Control functions     -   Local protection functions     -   User Interface         The system platform is Microsoft Windows XP Professional. The         software development platform is Microsoft Visual .Net. The main         programming language is C++.

The major control system runs on an event driven mechanism, wherein each module communicates with others through the event engine. The advantage of the approach is

-   -   Minimize global variables to improve system reliability     -   Modularize each sub system and make whole system scalable     -   Easy for debugging

Due to the time constraints, the UIC module will run on an interrupt based module. The interrupt will activate 720 times per second, it will receive data from PMU and check whether they satisfy IEEE 1547. In case of emergency, an emergency handling module will be called to control the DG unit directly, otherwise, event information will be sent to the event engine.

As shown in FIG. 73, there are several major functional blocks in the main system controller of the present embodiment: an event engine, HMI, supervisory control, engine control, generator control, local protection, and I/O card API. These functional blocks will control part of the hardware through the API to get inputs and send output information. These functional blocks communicate with each other by sending events and receiving events from the event engine.

5.2.2 The Structure of the Event Engine and Sub Module

As mentioned before, different functional blocks communicate with each other through events. Following is a definition of the event.

struct sysEvent {   unsigned short sysPriority;   unsigned short sysObjectFrom;   unsigned short sysObjectTo;   unsigned short sysCommand;   union   {     struct     {      int iHigh;      int iLow;     } Integer;     long longInfo;     float floatInfo;   } message; };

The event engine is a FIFO event queue. Each module can push events to the queue, and the engine will send the events to every module to check.

class sysEventQueue {   protected:     static sysEvent eventQueue[MAX_EVENTS];     static int sysQueueHead, sysQueueTail;   public:     sysEventQueue ( );     ~sysEventQueue ( );     static void putEvent (sysEvent event);     static void replaceEvent (sysEvent event)       { eventQueue[sysQueueTail] = event; }     static void getEvent (sysEvent& event);     static int isEmpty ( ); };

Each submodule will be a class inherited from the class of sysObject. The major module in the class is the handleEvent function, the function that will execute normal monitor functions and communicate with other modules by sending events to the event engine and handling events from the engine.

class sysObject {   Private:     unsigned short objectType;     unsigned short objectID;   public:     sysObject ( ) { };     ~sysObject ( ) { };     virtual void handleEvent (sysEvent& event) { }     virtual void clearEvent (sysEvent& event)       { event.sysCommand = evNothing; }     virtual void pushEvent (sysEvent& event)       {         sysEventQueue::putEvent (event);         clearEvent (event);       } };

5.3. Phasor Measurement Unit (PMU) Development

5.3.1 Hardware

The Phasor Measurement Unit (PMU) acts as an interface that converts the standard substation measurements into digital measurements that can be processed by the controller. To attain a higher rate of data transmission between the PMU and the controller, a CAN bus will be the media connecting them. The circuit diagram is as shown in FIG. 77.

The PMU control software was developed using assembly language and implemented in a PIC16C773 chip, which is shown in FIG. 74. Specifications of this exemplary PMU include:

-   -   Sampling rate: 720 samples per second per channel.     -   Sampling resolution: 3 channel 12-bit A/D converters.     -   4K-Byte program memory and 256-Byte data memory.     -   2 Timers except watchdog timer.     -   1 CAN port.

5.3.2. Testing of Prototype PMU

An SR 232 interface was developed to test the functionality of Phasor Measurement Unit (PMU). It includes an SP232 chip and four 0.1° F. capacitors. The purpose of introducing the interface into the test is to convert the CMOS outputs into the correct SR 232 signals. Thus, the computer can poll the outputs of PMU via its serial port. To poll data using a computer via its serial port is only a method to do testing. Some embodiments of the PMU do not include serial communication capabilities, implementing CAN communication instead. A block diagram of this subsystem is shown in FIG. 75.

5.3.3. PMU Software Re-Development

The PMU algorithm in one embodiment included a flaw, in that it did not consider accumulated errors caused by truncations and iterations. The new algorithm does its calculations recursively, which causes the accumulated errors, and non-recursively at the same time. After each cycle, the non-recursive results are copied to replace the recursive ones, thereby eliminating accumulated errors while still keeping the efficiency of the old algorithm.

5.3.4 Converting Coefficients into Phasors and Frequencies

The outputs of PMU are sine and cosine coefficients. More calculations based on these coefficients are needed to yield phasors and frequencies. In various embodiments, this conversion is implemented using a Visual Basic program or using C++ consistent. The code for one embodiment is provided in Appendix B.

A diagram showing the frequencies vs. time is shown in FIG. 76. The average of frequencies is very close to 60 Hz.

6. Additional Improvements

6.1. System Controller

6.1.1. Summary

The following activities have been accomplished:

-   -   Tested digital analog I/O board     -   Developed protection module and implemented PLC function in VC++     -   Developed engine/generator control module in VC++     -   Developed DG unit control function in VC++     -   Developing system controller user interface in C++

6.1.2. Protection and PLC Function

Some protection functions were implemented in a PLC module in some embodiments because sufficiently low-level access to the system controller was unavailable. In another embodiment those functions were implemented in and will be incorporated into a new controller. The code for the PLC is attached in Appendix F.

6.1.3. Engine and Generator Controller

Following is an example of a method of calculating.

To calculate Voltage Bias

percent_ref = 10; // +/− 10% of reference voltage volt_range = 9; // +/− 9 Vdc of voltage bias ref_voltage = 480; // normal voltage 480 Vac detected_volt = 0; // initial value ----------------------------- volt_bias = 0; max_volt = 0; min_volt = 0; Find  limits  of  volt ${max\_ volt} = {\frac{\left( {100 + {percent\_ ref}} \right)}{100} \times {ref\_ voltage}}$ ${min\_ volt} = {\frac{\left( {100 - {percent\_ ref}} \right)}{100} \times {ref\_ voltage}}$ If (min_volt ≦ detected_volt ≦ max_volt) ${volt\_ bias} = {\frac{\left( {{detected\_ volt} - {ref\_ voltage}} \right)}{ref\_ voltage} \times {percent\_ ref} \times {volt\_ range}}$ Elseif (detected_volt < min_volt) ${volt\_ bias} = {\frac{\left( {{min\_ volt} - {ref\_ voltage}} \right)}{ref\_ voltage} \times {percent\_ ref} \times {volt\_ range}}$ Else ${volt\_ bias} = {\frac{\left( {{max\_ volt} - {ref\_ voltage}} \right)}{ref\_ voltage} \times {percent\_ ref} \times {volt\_ range}}$ End Return volt_bias To Calculate Speed Bias

The Throttle Position Sensor (TPS) provides a voltage signal that changes relative to the position of the throttle valve. Signal voltage will vary from less than 1.0 volt at idle to about 4.6 volts at wide open throttle (WOT). The TPS signal is an input used by the ECM for fuel control and for many of the ECM-controlled outputs.

kp = 1; // proportional gain ki = 15; // Integral gain imin = −100; // minimum value before multiplying ki imax = 100; // maximum value before multiplying ki kd = 0; // derivative gain max_power = 85000; min_power = 0; speed_range = 4; // speed range and offset show speed bias from 0.5 to 4.5 offset = 0.5; needed_power = 0; // needed power from power management present_power = 0; // power that this generator is producing freq = 60; // frequency rad_speed = 0; // omega rad/sec ref_torque = 10; feed_back_torque = 0; error = 0; pterm = 0.1; istate = 0; iterm = 0; dterm = 0; old_error = 0; pid_result = 0; instant_power = 0; speed_bias = 0.5; if (needed_power == 0) speed_bias = 0.5 else rad_speed = freq × 3.14159 ${ref\_ torque} = \frac{needed\_ power}{rad\_ speed}$ ${{feed\_ back}{\_ torque}} = \frac{present\_ power}{rad\_ speed}$ // PID Control error = ref_torque − feed_back_torque //Calculate Proposition term pterm = kp × error; //Calculate Integral term if (istate > imax) istate = imax; if (istate < imin) istate = imin; iterm = ki * istate; // some papers use iterm = ki * (istate + error) // Calculate Derivative term dterm = kd * (error − old_error) // Remember old data old_error = error; istate = istate + error; // PID output pid_result = pterm + iterm + dterm; //Calculate Power for Throttle position need instant_power = (ref_torque + pid_result) × rad_speed; // Check for security If (instant_power > max_power) instant_power = max_power; if (instant power < min_power) instant_power = min_power; //Calculate Speed Bias ${speed\_ bias} = {{\frac{instant\_ power}{max\_ power} \times {speed\_ range}} + {offset}}$ End Return Speed_bias

6.1.4. Updated System Controller Schematics

The functional diagram of a system controller in FIG. 73 has also been applied in a second embodiment. There are seven major functional blocks in this main system controller: event manager, HMI, supervisory control, engine control, generator control, local protection, and I/O card API. These functional blocks control part of the hardware through the API to get inputs and send output information. These functional blocks communicate with each other by sending events to and receiving events from the event manager. The UIC communicates with the event manager through an event loop or an interrupt.

A test unit was placed in a test cell. A computer controller was connected to the unit through the digital and analog I/O card. Testing included three major tasks: I/O connection testing, functional module testing, and integrated system testing. I/O connection testing checked each input signal and each output signal to make sure that they were correctly connected and respond properly. Functional module testing tested each software module described in the previous section and performed functions as designed. Integrated system testing tested the system as a whole.

6.2. Utility Interface

6.2.1. Summary

The following research and development activities have been undertaken:

-   -   Tested the stability/reliability of PMU by running it         continuously for approximately 50 days.     -   Developed CAN communication.     -   Revised PMU Assembly code for the CAN communication.     -   Programmed UIC functions in VC++.     -   Compared compliance of existing technology with IEEE 1574     -   Refined and tested the UIC functions.     -   Constructed a PMU unit.     -   Developed HIF detection technology

6.2.2. Test of the Stability and Reliability of a Prototype PMU

Overview

Since the PMU units will be running continuously for months once put into use in practice, a prototype PMU had been put online to test its stability and reliability. The data the PMU acquired were transmitted to a PC via SR 232 communication. A VB program running on the PC converted data into meaningful variables with time stamps and recorded them on the hard drive.

Test Results

Analyzing a small portion of the recorded frequencies showed that there were no frequencies that were apparently absurd. This initial result indicated that the PMU worked properly during the test. It also indicated that the PMU assembly code is stable and reliable.

6.2.3. Development of CAN Communication

Overview

In this embodiment, the Phasor Measurement Unit (PMU) acts as an interface that converts the standard substation measurements into digital measurements that can be processed by the controller. To attain a higher rate of data transmission between the PMU and the controller, a CAN bus is used as the media connecting them.

Schematics

The circuit diagram is shown in FIG. 78.

Code for CAN Communication

CAN communication is implemented using PIC18F4580 chips. MCP2551 is used as CAN transceiver. The assembly code running on the PIC18F4580 for CAN communication is shown in Appendix D.

6.2.4. Revision of PMU Assembly Code for CAN

Overview

After successful testing of the functionality of Phasor Measurement Unit (PMU) with RS-232 interface, PMU with CAN bus interface had been developed as a final design. In this design two PMU units are connected to the PC via a CAN bus.

PMU sends calculated phasors to a CAN chip using Parallel Slave Port (PSP). We used PSP instead of serial posts to achieve fast data communication. The CAN chip sends this data to PC using CAN bus. A CAN transceiver is used between the CAN chip and the CAN bus to convert voltage levels. Synchronization between the PMUs is a challenging task in this project. To achieve proper synchronization, one PMU works as the master PMU and all others (in current case only one) are slave PMUs. The master PMU will send synchronization pulses to slave PMU and slave PMU will use this pulse for synchronization.

After analyzing data transmitted to PC, we can see good synchronization between both PMU. Results will be better after using filters.

Schematics

The circuit diagram is shown in FIG. 79.

Code

The current version is developed to address the practical CAN communication. Since more than one PMU shares the same CAN channel, the first revision is to incorporate an id number into the data each PMU sends to the computer. Therefore, the PC can distinguish and assemble data correctly. Since we also need to make all PMUs sample at substantially the same instant, the second revision is to introduce a master PMU and let all others be slave PMUs. The master PMU will send synchronization signals to slave PMUs to guarantee the substantial simultaneity of corresponding samples on all PMUs. This improves the operation of the UIC and other control functions. The code is attached in Appendix B.

6.2.5. Programming of UIC Functions in VC++

The UIC functions were programmed for simulation using Matlab, then were rewritten in VC++. The new version also generalized some cases and provided many default parameters. The code is in Appendix E.

6.2.6. Comparison of Compliance of Basler and Woodward Productions with IEEE 1574

One current system uses a Woodward EGCP-2 as the Genset controller and a Basler relay as the UIC. The newly developed integrated controller meets the IEEE 1574 requirements into the product.

The following table compares the Basler relay's characteristics and requirements of IEEE 1574.

Requirement IEEE 1547 Standard Basler Relay Synchronization Δf = 0.3 Hz Δf = 0.01-0.5 Hz ΔV = 10% ΔV = 1-20 V Δ{acute over (ø)} = 20 degrees Δ{acute over (ø)} = 1-45 degrees Voltage V < 160 → 0.16 sec Pickup: 10-300 V disturbances 60 < V < 106 → 2 sec Time delay: 0.05-600 sec 132 < V < 144 → 1 sec 144 < V → 0.16 sec Frequency F > 60.5 → 0.16 sec Pick up: 40-70 Hz disturbances 59.3 > F > 57.0 → user Time delay: 0-600 sec F < 57 → 0.16 sec Disconnection of Overcurrent protection Time overcurrent faults and ground fault protection available with protection pick up to drop out ratio = 95% Surge withstanding Comply with conditions Complies with IEEE capability of ANSI C62.41 or IEEE C37.90.1 C37.90.1 Influence of EMI Not influenced by EMI Qualified to C37.90.2 Prevention of Has a reverse power unintentional protection which can be islanding used to prevent islanding Inadvertent Area EPS Voltage and Recloses between 100 energization frequency must be in the milliseconds to 600 range 106 V-132 V and seconds 59.3 Hz-60.5 Hz. Reconnection can be delayed up to 5 minutes after EPS has regained normalcy Measurement of All the 3 phases need to All 3 phases are Voltage current and be measured measured Frequency The following table shows the comparison of Woodward EGCP-2's characteristics and IEEE 1574

Requirement IEEE 1547 Standard EGCP2 Synchronization Δf = 0.3 Hz Δf = 0.01-0.5 Hz ΔV = 10% Volt window = 0.1-10% V Δ{acute over (ø)} = 20 degrees Default Voltage: 10% Δ{acute over (ø)} = 2-20 degrees Default Δ{acute over (ø)} = 10 degrees Voltage V < 160 → 0.16 sec Pickup: 50-30000 V disturbances 60 < V < 106 → 2 sec Default 132 < V < 144 → 1 sec Pickup(high): 250 V 144 < V → 0.16 sec Default Pickup(low): 200 V Time delay: 0.1-30 sec Default time delay: 5 sec Gen volt Hi limit: 10% above rated Gen volt low limit: 10% below rated Frequency F > 60.5 → 0.16 sec Pickup: 40-75 Hz disturbances 59.3 > F > 57.0 → user Time delay: ? F < 57 → 0.16 sec Default Pickup(High): 65 Hz Default Pickup(low): 55 Hz Disconnection of Overcurrent protection Pick up: 5-30000 A faults and ground fault Default pickup: 30 A protection Delay: 0.1-20 sec Default delay: 1 sec Surge withstanding Comply with conditions Complies with IEEE capability of ANSI C62.41 or IEEE C37.90.1 C37.90.1 Influence of EMI Not influenced by EMI Qualified to C37.90.2 Prevention of No islanding feature unintentional islanding Measurement of All the 3 phases need to Only 1 phase of the Voltage current and be measured utility is measured and 3 Frequency phases of the Genset is measured Voltage Regulation Must not degrade Does not degrade customer voltage beyond voltage beyond 2-5% + or − 5% of nominal of nominal voltage voltage

6.2.7. Test and Refinement of the UIC Functions

In this experimental embodiment, the overcurrent relay function has been integrated into our main UIC function. The development of ground fault detection function is being developed as a standalone relay function independent from main UIC functionality.

6.2.8 Development of HIF Detection Technology

High Impedance Fault (HIF) is a concern in the implementation of DG, even though it has not yet been officially addressed by the IEEE Standard 1547. An HIF condition occurs when a device (and, perhaps, a portion of the utility grid) becomes electrically isolated from the remainder of the grid. When the device (or portion of the grid) is not electrically isolated from the remainder of the grid, the device is in a “non-HIF” (non-high-impedance-fault) condition. For public safety and the potential huge expenses resulting from an energized downed conductor, DG operators should pay some attention to HIFs. We have developed a Decision Tree (DT) based technology that addresses this concern. It showed excellent performance in a simulation study. FIG. 80 shows a one-line system diagram based on which HIF-related simulations have been performed.

With the integrated controller, the Decision Tree (DT) based detection technology can use a simplified version of PMU to provide raw current data samples. DTs are typically trained off-line from simulated HIF and non-HIF data first, then are tested and trained using experimental data to further improve performance. The DT for use with the present system uses only current signals measured at Point of Common Coupling (PCC), though other electrical characteristics are used in alternative embodiments. Current harmonics are also used to train the DTs. The DTs apply the training to real data that characterizes the current (or other characteristic) at the PCC to determine whether or not a HIF condition exists, and provides an HIF Detection Output as a function of that determination. The DGSC receives the HIF Detection Output and modifies operation of the DG system accordingly, as discussed herein. Simulations of this subsystem were done with the aid of the Electromagnetic Transients Program (EMTP).

While the system and methods have been illustrated and described in detail in the drawings and accompanying description, they are to be considered as illustrative and not restrictive in character, it being understood that the preferred embodiment has been shown and described and that changes and modifications that come within the spirit of the invention are desired to be protected. 

1. A distributed power generation system adapted to interface with an electric utility distribution system at a point of common coupling, comprising: a plurality of distributed power generation resources, collectively having an aggregate output rating; and a controller; wherein the distributed power generation resources export power at a first time to the electric utility distribution system, and wherein, if a first portion of the electric utility distribution system that includes the distributed power generation resources becomes electrically disconnected from the remainder of the electric utility distribution system, the controller causes the distributed power generation resources to export power to the first portion of the electric utility distribution system for not more than about two seconds.
 2. The system of claim 1, wherein the distributed power generation system complies with IEEE Standard 1547, section 4.4.
 3. The system of claim 1 wherein, while the first portion of the electric utility distribution system is electrically disconnected from the remainder of the electric utility distribution system, the controller prevents the distributed power generation resources from beginning to export power to the first portion of the electric utility distribution system.
 4. The system of claim 1, further comprising: a decision tree that is trained at least in part on training data characterizing the electrical characteristics during HIF and non-HIF conditions at the point of common coupling, then configured to accept real data characterizing the electrical characteristics at the point of common coupling and provide an HIF detection output; and a control system that modifies the operation of the distributed power generation system based on the HIF detection output.
 5. The system of claim 4, wherein the training data and real data are measurements of one or more currents at the point of common coupling.
 6. A distributed generation subsystem that detects islanding of the subsystem, comprising: a plurality of generators that produce AC output power for a load, in parallel with a power grid that has a first frequency characteristic; and a controller that controls the output level of each of a plurality of generators using one or more control signals; wherein the controller superimposes a perturbation signal on the control signals, the controller detects the frequency characteristic of the AC output power; the effect of the perturbation on the AC output power has a second frequency characteristic that is detectably different from the first frequency characteristic; the controller produces a first signal if the detected frequency characteristic is sufficiently like the first frequency characteristic, and a second signal if the detected frequency characteristic is sufficiently like the second frequency characteristic; in response to the first signal, the controller allows export of power from the generators to the power grid; and in response to the second signal, the controller ceases export of power from the generators to the power grid, if such export is occurring when the second signal begins to be produced, and prevents export of power from the generators to the power grid while the second signal is being produced.
 7. The subsystem of claim 6, wherein the cessation of the export of power from the generators to the power grid occurs within two seconds of the time at which the second signal begins to be produced.
 8. The subsystem of claim 6, wherein the cessation of the export of power from the generators to the power grid occurs within two seconds of the time at which the frequency characteristic sufficiently like the second frequency characteristic begins to be detected.
 9. The subsystem of claim 6, wherein the controller comprises a supervisory controller and, for each generator, a subordinate controller that receives control signals from the supervisory controller and controls the output level of that generator. 